{"group":{"id":1,"name":"Community","lockable":false,"created_at":"2012-01-18T18:02:15.000Z","updated_at":"2026-04-16T00:12:35.000Z","description":"Problems submitted by members of the MATLAB Central community.","is_default":true,"created_by":161519,"badge_id":null,"featured":false,"trending":false,"solution_count_in_trending_period":0,"trending_last_calculated":"2026-04-16T00:00:00.000Z","image_id":null,"published":true,"community_created":false,"status_id":2,"is_default_group_for_player":false,"deleted_by":null,"deleted_at":null,"restored_by":null,"restored_at":null,"description_opc":null,"description_html":null,"published_at":null},"problems":[{"id":47108,"title":"Get the side length by using the law of cosines. ","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 228.75px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 114.375px; transform-origin: 407px 114.375px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 122.55px 7.25px; transform-origin: 122.55px 7.25px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eSuppose we have a trianlge like below. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 138.75px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 69.375px; text-align: left; transform-origin: 384px 69.375px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" style=\"vertical-align: baseline;width: 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\" data-image-state=\"image-loaded\" width=\"220\" height=\"132\"\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 78.5833px 7.25px; transform-origin: 78.5833px 7.25px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eCalculate the side length \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ec\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 20.6167px 7.25px; transform-origin: 20.6167px 7.25px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e when \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ea\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 7.25px; transform-origin: 3.88333px 7.25px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eb\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 46.2917px 7.25px; transform-origin: 46.2917px 7.25px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and the angle \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eγ\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 50.9583px 7.25px; transform-origin: 50.9583px 7.25px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e(deg) are given. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 180.467px 7.25px; transform-origin: 180.467px 7.25px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eRefer to this page for more details on the law of cosines. : \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://en.wikipedia.org/wiki/Law_of_cosines\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003ehttps://en.wikipedia.org/wiki/Law_of_cosines\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = law_cos(a, b, gamma)\r\n  y = a;\r\nend","test_suite":"\r\n%%\r\na = 1;\r\nb = 5;\r\ngamma = 45;\r\ny_correct = 4.350739269151224;\r\nassert(isequal(law_cos(a, b, gamma),y_correct))\r\n\r\n%%\r\na = 3;\r\nb = 4;\r\ngamma = 90;\r\ny_correct = 5;\r\nassert(isequal(law_cos(a, b, gamma),y_correct))\r\n\r\n\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":658698,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":63,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2020-10-28T08:02:26.000Z","updated_at":"2026-03-15T03:58:26.000Z","published_at":"2020-10-28T08:02:26.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSuppose we have a trianlge like below. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"132\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"220\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCalculate the side length \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ec\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e when \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ea\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eb\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and the angle \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\gamma\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e(deg) are given. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eRefer to this page for more details on the law of cosines. : \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://en.wikipedia.org/wiki/Law_of_cosines\\\"\u003e\u003cw:r\u003e\u003cw:t\u003ehttps://en.wikipedia.org/wiki/Law_of_cosines\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/image\",\"target\":\"/media/image1.png\",\"relationshipId\":\"rId1\"}]},{\"partUri\":\"/media/image1.png\",\"contentType\":\"image/png\",\"content\":\"data:image/png;base64,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\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"}],"problem_search":{"errors":[],"problems":[{"id":47108,"title":"Get the side length by using the law of cosines. ","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 228.75px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 114.375px; transform-origin: 407px 114.375px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 122.55px 7.25px; transform-origin: 122.55px 7.25px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eSuppose we have a trianlge like below. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 138.75px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 69.375px; text-align: left; transform-origin: 384px 69.375px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" style=\"vertical-align: baseline;width: 220px;height: 132px\" 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qlLlx/uPLPcNOmqeTQAfBqptR46KpgQnhQo3bL+SdaSlBRgRnK3hzZyu+LJR87aUQxSlyuP7jwx/HHTUnzmQdMuN7r9FRAlOChO+IZ4cor/McGbo+AaWm0Kn7GvnbSmnKEqVewZ/JnmTVwcd1YDXf6wJJpFRgpPCmAEtAoOvuDDDTgJmBGfdNHBVgZ+o5m2JQ7GlyvRqUdvRkHHEdDsG2//3Osm7+oUtKkpwkr+pdjgDd3k+JeO46XYMSX4JwT9swxdZZP5RwCeqeVviVEypMjUbMsEoDs84YgTX4BYlB3ie2827hQQp21KCk/yNZH/SO1HcDLTSYf8jmBLttNkpDOe3pG6cWy6n0/y8gE9T87bErZhS5Q39R4bvM8Pu3X/eaifQbm/EMh14J3hU5ckIabFlyV+7PRvDjwGwdJDgKCxfwP0jfQU3+WPXYPRmDF+h01yd56ckgEuBi3B/Tx/DXSmqv03ishC3rc5aXFVh6G113PJbtwNTg0eSuNVMNgJ74XYPmInbpqcBeAZ4EstLdJmLow2//ugKTgqRvv/WwDN0mi9i+QzwNO4ehdtdwPBdYFIByU3N21KJ8i9V+qaPsZyM4Uu4q7NNuO1wNgHfYBj7kWQT9N+fc/esE7w/6uBFJH7NuC8CC/SRTnIilWAa7u+mRTuAi0geWnCbbFpcufOkWKMRyWwh7u9oN6XYVkdEas5coAf3xbGK1LYhIpVnHO7emSW9SaqIyDZSzdupss+9pKdMi1QqlSpFJKsJwP2kvyiuId1+IFLpVKoUkYwmA3/FfUFsJt1nJFItVKoUkW20AutxXwxvAMfEG45IwVSqFBEgvfN2EveF8CiwW6wRiRRPpUqROjcK6CT9225X8JhItVOpUqSONaPmbaltKlWK1KEW1Lwt9UGlSpE6ouZtqScqVYrUATVvS71SqVKkhql5W+qdSpUiNUjN2yIqVYrUHDVvi6SpVClSA9S8LZKZSpUiVUzN2yKDU6lSpEo1o+ZtkaGoVClSZVpQ87ZIrlSqFKkSat4WyY9KlSIVTs3bIoVTqVKkQql5W6R4KlWKVBg1b4tEQ6VKkQqi5m2RaKlUKRIzNW+LlI5KlSIxUfO2SGmpVCkSg2bUvC1SDipVipRRC2reFiknlSpFykDN2yLlp1KlSAmpeVskXipVipSAmrdFKoNKlSIRUvO2SOVQqVIkImreFqk8KlWKFEHN2yKVTaVKkQKoeVuk8qlUKZKnZtS8LVItVKoUyVELat4WqTYqVYoMQc3bItVJpUqRQah5W6T6qVQpshU1b4vUDpUqRQJq3hapLSpViqDmbZFapVKl1C01b4vUPpUqpe6oeVukPqhUKXWlGTVvi9QTlSqlLrSg5m2ReqRSpdQ0NW+L1C+VKqUmqXlbREClSqkxat4WkTCVKqUmqHlbRLamUqVUPTVvi8hgVKqUqqTmbRHJhUqVUlXUvC0iuVKpUqpGM2reFpH8qFQpFa8FNW+LSGFUqpSKpeZtESmGSpVScdS8LSJRUalSKoaat0UkaipVSuzUvC0ipaBSpcRKzdsiUkoqVUrZqXlbRMpFpUopGzVvi0g5qVQpZdGMmrdFpPxUqkRftqXUAvjAzsA63F+yX8UZkIhEy7a1HYAxczDmSGBvXHVmNcb8BmsvN77/WozhLQRmAmtxk9vijCUWSnClMRe4Gjf1/0XgFODJWCMSkUhZz5sN/BT373wd1v6aRMJg7anAMOAdjGk1nZ33xRTiuKZE4rmeZHLcjk1N963t6flITHHERgkuWk3AdaSn/i8DOoC3YotIRCJnTzvtPfT1PQ+MBFbT0HCUuemmVwHsjBlHkEzeGzy3ATjc+P7TZY2vre1DJBKX3v7666dMf+CB1Pf8LGBBOeOIWyLuAGrIBNxqJKnkdi3wSZTcRGpPb+9ncAkMjPlKKrkBmMWL/wB8LTgdhVuxqCys5423nvcLEomVQOu097zHnjBhwkvB09dRZ7MqleCiMRl4CDgW2AKcC1wA9MYZlIiUiDEfC456GT78lgwjfkD6l9tjbFvbwaUOyXZ0zMTdCpmN+25/EGuPvW/NmkNxfbc7BnHVDSW44rXiktv7gb8DHwWujzUiESm1/YI/XzDz52/Y+knj+xuBR/ofSCQmlyoQe+qpu1rPuwNrFwITcZNcphvfP9p0dT2IS7SpytI06mhWpRJc4VLN20uA0cBjwKHA7+MMSkRKy7a0NOJmR4PrNxtMT/+RMe+WJJaOjuNoaPgjcGLwOQtobDzYdHbevtXQ24FFwXHdlCq1wG9hRgE/A7zgfAlwJu6GsojUsvHjR4TONmYZuVf/UV/fE1GGYOfNS/DUU5di7UW4yYKvYcxZprPzriwvOx84AXeV9wNgepQxVSJdweWvGXgAl9ySwMXBsZKbSD3o6QlfGNhMQ2xb2xTgQ8HpPWbJklVRfbydM2cEK1cuxJjUwhHLaGw8ZIjkBnVYqtQVXH5aUPO2iGRhPe9E4Ibg9ClgTmTv3do6jg0b7gAOA5IY81U6O68wgyTaDFKlypm4UuVyargBXAkud2reFpGMrOd9HTgcN6N6T9wvwJcBlxnffyeSz5g5c2d6e+/A3evvAc4ynZ3zC3iruilVqkQ5tNTO29/DJbdluN+elNxEJOU44FO45Abuu3UKxsyy06aNLPbN7cyZu9Db+3tccluHMZ80vl9IcoM6KlUqwWWn5m0RGZLx/Y8Z3zcMG7YDicSRGPMT4GisvY4RI54N7skVxHreaHp7lwL74O71fyqC5b/qYlalluoa3GTgVlx/2xbcZb3620TqnD3llB1pauoOTn9tfP+kjOPa24/CmHuBEcB6kslDzJIlz+f1WZ7XAPwa94v1FqydZrq6/q+Y+EPG4e4RTsQlvJorVeoKLjM1b4tIUUxX14MYc2VwOgZjvpX3m1h7CS65JTFmdoTJDeqgVKkEN5Cat0UkOsYsDh1Pt+ec05TrS63ntWPMRcFrv2k6OzujD7C2S5VKcGmjgJtIb0q6BDgeWB1nUCJSxSZNehrXLwswgu7uvbINT7GnnbY7rtXAYG0nnZ3/XaoQcbdfanKtSiU4pxk1b4tIxMy8eUlgff8D1u6Y0wv7+q4FtgdeY9iwz+XR51aImi1Vqg8uouZt63mtwOnAFGB88PCrGLMMY/7HLF781/6x7e3fwJh5wA3G988uLnwRqVTBJJHR/Q80NKzL4TXtuD5bgHPNwoXd2cZHpCYbwOv9Cm4ucDcuub2I2+4mr+Rmp00baT3vTuBmoB33W9edwOPAXlh7LsnkCtvWdiiA9bzzguT2LMb8LLL/EhGpPNZOARqCs3dJJv+adbjnbQdcGbz258b3f13aAAeouVJlvSa46Jq3R4xYhJvlBHAXPT3Nxvdbje8fjbVfDh4fTSJxfXCD+WvAO8AJprPzgSL/O0SkQlkwGPON9APWD7bRGZxbX3JPYC3G/GdpI9xGzZUq6zHBDWjenjhixM8psHnbdnS0ke4deZZNm041S5eu7R8wefKVQGqr+oPp7j4f2BW4zvj+GwX/F4hIpZhoPW/01g/a008fS0fHfOATwUOrMebibG9kW1vHYe2F7sReYXz/zcijHVpNzaqst3tw/c3bBnq+NXnyC1+dNOnjNDWNKajObe2XQsffMrffPmDPJzNvXtJ2dPhYm/ot7usAJJO/LPQ/QEQqyiHA69bzfgu8FDzWTE/PCbiZ2QC/A84c8pfapqZ/w9rRwN8YPfrqEsWbi5pZq7KeruAGNG9/eOzY1q9OmrQT8B62bLk23zeznjcROCp1Sm/vYLXyu0PHOwCPmyVLns3380SkIr0BvIJrKfo8rjJ0BPAM8AOM+Yjx/eOM77+Y7U3s7NmjsPYLABhzjbnxxk2lDTurmilV1sMVXAK4FEhtDPgYcMpj3d2rsfZCjPklxpxhPe9Hxvdzb+g25jBs/8zd1weUJsM2bnyCESN6Sf+/XlDgf4eIVJ7HBluqKy+bN88AdgI2YO2Pi36/4tXErMpav4LL2rxturoWAPcEz/2PzW9tznBtes1gg4Ky5crQQ3fm8RkiUg+snR38udD4/tsxR5NS9bMqaznBNZNb8/Z/Bs8fQXt7ex7vH76xnL2cYO3DoeMPZRkpInXGtrW9H/eLNzQ0/DTeaAao+lJlrSa4FuAR4EBc8/bJwOVkWA3A+P4KUmVDY76S8yckk+tDZyOyjjUm3X6QSByVZaSI1JuGBg9XPXqBxYv/GHc4W6nqWZW1mODyb95OJL6Fu4o72La3fyLr2PRrXg+djR90nHN4/5G1R+f0/iJSH6w9Kfizs8RLchWqakuVtZTgCm7eNosX/4XUvTFj5ub0adY+Ejp7rz3jjO0zDps6dTju8j7lw3bOnOxXfCJSF2xr6zjgSAASid/EG82gqrZUWSsJrvidt41JtQpMta2tE4Yc7npaHkydsmVL5iu/0aPbcL/5pFYwGMa77x6ecayI1JeGho/glvJ6hzVrKq08GVaVpcpaSHCTcf1tx+J23j4XuADozetd9t33buBVoJHGxlk5vcba74TOvrT1LEw7b14CuBBYjzE/Cj11Yl6xiUjFMEuXrjW+b4KfYlsEjgn+XG6WL8/vO6v8qq5UWe0JLrKdt4NtLW4KTnOaTWm6um7GLbIMcCTt7VcMSHJPP30x8GGs/RnG3ECqvm7tWdbzDrIdHR+znrekkHhFpAYYcwQA1j44xMhKUHWlynz6vipJxuZtityc1M6YcRjJ5MNAkt7eXc0ttwza39b/Grf6982kr8qextr7MeZ9uDLpMzQ1HW0WLuy2nncx8O2t3uKfxvfHFBO3iFQfO3XqcEaPXgcMA1qM7/827phytBDXAL4WV0Gr2AbwaryCK93O25MmPYZr2k7Q1PTRXF5ifH8jvv8vwL/iuv13xZhPA3sBV7F585TUOpfG9y/DmI9jzALgN1h7KQ0N+xYdt4hUn5Ej98UltySbNz8edzh5qLpSZbVoBlbgSn19pJNcZGxHxyLredZ2dPwwyvcVEQmzHR0d1vOs9byX446lANNw38OWCi5VVtMVXAs5Nm8X6SEArD0s4vcVEQn7YPBn1k1QK1RVzKqslgRX9M7beXgs+HNy0MMmIhK9ZPIDABhTjQkOqqBUWekJLrqdt3O1adOTuKvCYWy//V4l+xwRqW/GuKueZLIaS5RQBbMqKznBFd+8XQBz223rAbeTbl9fcyk/S0TqmltQwpghZ2tXsIouVVZqgoumebtwrwCQSOxZps8TkfqTWsP2zVijKF7FliorMcFF1rxdhNRCyhPL/LkiUj92BsDaf8QcR7EqtlRZSQkuAVyG62sbjZvscSiQ+y7bUTHGbYWTTI4q+2eLSM2zLS2NpLbZamhYF280kajIUmWlJLjSNW8XIpl8FwBjlOBEJHq77x6eob0ltjiiVXGlysa4AwB2BW4BpgTnPvD/gF3iCujh7u7hOw8fztqenvG4UqmISGROvvfeHa4+6CAAfrxq1S7A5ngjisx3cZW4aYCH+z6PTZSrgJyEu0wF+Anw2RxeMwx4HtgjwjhERCR+a4DdGfoK9VDcIh652gx0A38GlgI/BTZlGhjVFVwjcGXo/KAcX2eozB1sRUSkOBvJ7SJqBLA4OD4U+EBwvAJ4LjSuAdgJt5rVxODn47hZ9sfjFn8eIKoruH8Hrgmdb8JNFOnL4bXDgZERxSEiIpXhXfIvvd4FpDaPbsVdoW2tEXe/76rQY1cDX8o3wFyMxU0TXU968U0LaJV8ERHJxxrSOWT3IcYuD439U6YBUcyi/DrusvFsBpYbcy1TioiIvJeBze+vDjH+xdDxsEwDik1wewGfxy18vBh4KfTcgUW+t4iI1I+DQ8ePDToqLXyF92KmAcVOMrkSd9WWqn0+AbwvONYVnAjAPJvgadqxnIprh0m1wKwB/oTlLvro4paqXpNQpFjhnDFUgtsBOCp0fkemQcVcwZ0ATMdNLnk+eOyJ0PO6ghOZYQ9jJSuxLMbtYfgUhp/gKh59wHQM36eRl/HsebHGKhKvfK7gvg5sFxy/BK3HUQoAAAPxSURBVPwsykASuGT2N2BM6PGTGDjRRGs5Sv3qsB14djOetXj2Lk61uw54fp5N0GF/GDxvabcXxRSpSCVYRTp3DNYbPR63s0xq3F+ASYO9YaFtAmfhmrk/w8DM+V4GLq81FbizwM8QqV6e/Qju734T8ADwEXyzbcOrZ3fALe49EvgEvrm7nGGKVIgdSPexWaBzq+dH4JLeAUAP8ChuScf/JeKlzkbj/kE+TOYEGZ7m+eUoP1ikKky3Y/Dsy8GVWQ+e/WDW8Z59Es9aZtqdyxShSKU5noHVv2w/q3Crlxw71JsWcg/uYlzp8d/JvArJitCxJppI/RnB+aRKLIbF+OaFrOMtPwWuYpGp9m1TRAoVvv92De7iKfwzDDdrchbuiu3TwP24RZ0j2zRgd1x3+vwsYy4nnWmfjuqDRarCPJvAs6v776t59sS4QxKpAj8nnTfmDDF2LG7+R2r8vw02MN/Mdxlu5le20mN4JuXepGe6iNS+ZziE9F5Ym/kn98UZjkiVCF/BZVyVJKQbt71ayqAL++fTBzcFmIm7/3ZtlnE7hY4bgP1x9+tEal8fx4XuTD/OHaZWtkERKZXhpGdC9pJb5e+10PGg97jzSXBX42qh7wXa8njdgSjBSf1IT2+2PBNjHCLVYjLpXPQsuS3QvGPoeONgg3ItUc4AjsTVRre++Zfp58+h12qiidQPE9qoN8HrMUYiUi3yKU+mhBfzH/SKL5cruBG4iSMryT65JGwlrjQJWtFE6omlJ1SizN6f49lh2GBrkO24j/lmQ0ljE6lM4QS3YtBRacNwbQUp9ww2MJcE90VgT+AUIJnDeHAJLuUAtLGp1IsEz/T/TbdMGGL0eRi+CzzFfA4ocWQilSpc5cvlCu400nM9tpBlma6hSpS7AF8BHgJuzeGDU54KHY8hvUOrSG0z3BI6++ig42bYDwBfAyyW88HoF0CpRwkGVvmGSnB7AFeEzr/LwAknebked+V1XJ6v24uBnef5TEoRqW4d9qehPriLMzx/dGilk22fF6kf+5DOE3/LMq4Bl0deDY3/FW4pvEFlWmprJ9z6XiZ4wy3AbcFzX8UtkzKYM4BpuKzshR5fATwHLMMlTZHaNdUOZzRduMXHAVZg+QOGEbgZY4cCG7BcSJf5UWxxisRjH+C/g+OJpO+nvcW299MacTnpIFyDN8A/cVdxl+L6sgeVKcGdgEtEmewIvJPl/X4FfCrL819m4OWlSO3qsB1YZuMS2jjcdObnsNxJIz/kJqNZllKPPo1bSzIXW3AJbTXu1tc9wFJcs7eIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIFOb/A4u3kV8IJmX/AAAAAElFTkSuQmCC\" data-image-state=\"image-loaded\" width=\"220\" height=\"132\"\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 78.5833px 7.25px; transform-origin: 78.5833px 7.25px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eCalculate the side length \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ec\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 20.6167px 7.25px; transform-origin: 20.6167px 7.25px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e when \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ea\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 7.25px; transform-origin: 3.88333px 7.25px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eb\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 46.2917px 7.25px; transform-origin: 46.2917px 7.25px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and the angle \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eγ\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 50.9583px 7.25px; transform-origin: 50.9583px 7.25px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e(deg) are given. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 180.467px 7.25px; transform-origin: 180.467px 7.25px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eRefer to this page for more details on the law of cosines. : \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://en.wikipedia.org/wiki/Law_of_cosines\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003ehttps://en.wikipedia.org/wiki/Law_of_cosines\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = law_cos(a, b, gamma)\r\n  y = a;\r\nend","test_suite":"\r\n%%\r\na = 1;\r\nb = 5;\r\ngamma = 45;\r\ny_correct = 4.350739269151224;\r\nassert(isequal(law_cos(a, b, gamma),y_correct))\r\n\r\n%%\r\na = 3;\r\nb = 4;\r\ngamma = 90;\r\ny_correct = 5;\r\nassert(isequal(law_cos(a, b, gamma),y_correct))\r\n\r\n\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":658698,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":63,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2020-10-28T08:02:26.000Z","updated_at":"2026-03-15T03:58:26.000Z","published_at":"2020-10-28T08:02:26.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSuppose we have a trianlge like below. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"132\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"220\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCalculate the side length \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ec\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e when \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ea\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eb\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and the angle \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\gamma\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e(deg) are given. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eRefer to this page for more details on the law of cosines. : \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://en.wikipedia.org/wiki/Law_of_cosines\\\"\u003e\u003cw:r\u003e\u003cw:t\u003ehttps://en.wikipedia.org/wiki/Law_of_cosines\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/image\",\"target\":\"/media/image1.png\",\"relationshipId\":\"rId1\"}]},{\"partUri\":\"/media/image1.png\",\"contentType\":\"image/png\",\"content\":\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAbgAAAEICAYAAAAtAOHGAAAABmJLR0QA/wD/AP+gvaeTAAAgAElEQVR4nO3deZhcVZ3/8fep7k5CFiCEhKAs7QIYCJssYadxJSMJNN23QyAZoiDIGAaVGUR/o2YeBYFBEMRRURSNSUjfDgRQgQFCRAFljUhYBMMWEIPQITFk6e46vz/Ora7bSXV1Lbfq1vJ5PU8/ubfqVNUXnqS+fb/3fM8BEREREREREREREREREYmSiTsAEal6RwInAicAuwMTgATwNvA88BhwD7AM2BxTjCIiIjmbBjwM2ODnZVwSWwLcFZzb0M8/gRuAw+MIVkREZCijgV/gklYSmA/sP8jYA4C7GZjoXi5DjCIiInmZAKzEJar1wNQcXtMA/B/pBHdLyaITEREpwE7Ak7gk1QMcm8dr9yed4P4r+tBEREQKt5R0krqogNe/Grz2X6IMSkREpBizSSe3F4CmAt7jd8HrJ0YYl4iISMEaGTgj8uwC32cUsENUQYmIiBTrdNLJbQMwJt5wREREonEH6QS3JOZYREREIjEceJd0gpsbbzgiIiLROJ6BTdoHxhuOSO4ScQcgIhXtA6HjJPBsXIGI5EsJTkSy2SN0/CpaLFmqiBKciGQzPHS8NrYoRAqgBCci2bwVOu6JLQqRAjTGHYCIVLQXQseFrECyA+kFmVN7w4mIiMRuJOk2gSQwLs/Xfy94bR9wSLShiYiIFOd60m0CF+Txumm4pGiBS0sQl4iISFHGAWtwieptYM8cXtMKbAxecytuTzgREZGKcyywDpewXgfayHwP/yBgAekrvhspbOcBERGRsjkEeIJ08noLtwXOUuBu4LXQc88DXjxhioiI5C+Bu3r7BfAcrjeuB5fsHgV+iJs1qRnaIiIiIiIiIiIiIiIiIiIiIrKN4QxcmFlERKTqHQasBl4CxscbioiISDRmkV6xxAKd8YYjIiJSnAbgCgY2dqeO1eAtIiJVaQJwP+mEdg2usXthcN4NvDe26ERERAowGfgrLpFtBs4JPTcO+Fvw3G3lD01ERKQwrcB6XAJ7Azgmw5hppK/szihfaCIiIvlLAJeR3tvtUWC3LONVqhQRkYo3CjczMnVV1hU8lo1KlSIiUtGagRW4RNUHfBkwOb5WpUoREalILcCbuAT1DnBSAe+hUqWIiFSUubg93iywCjigwPdRqVJERCpCE/Aj0qXFe3FJqhgqVYqISKwGa96OgkqVIiISi2zN21FQqVJERMoul+btKKhUKSIiZZFv83YUVKoUEZGSKqR5OwoqVYqISMk0U3jzdhRUqhQRkci1UHzzdhRUqhQRkchE1bwdBZUqRUSkaKVo3o6CSpUiIlKwUjZvR0GlShERyVupm7ejoFKliIjkpVzN21FQqVJERIaU2Hf77edT3ubtKKhUKSIigxo1Zdy45yh/83YUVKoUEZGMmgmatxPG2Mv239/2et6MmGPKl0qVIiIyQAuh5u2fHHLI76znWet5b1jPmxhvaHlTqVIilYg7ABEp2FzgbmBn4EXg2LP23rsV+DuwC7DUzpkzIsb48nU+blLMjsAPYo5FaoASnEj1STVvfw/X17YMOAx40ixa9A/gU8C7wBQ2bFhg582rln/nb5FuZ5iGSpUiInUlp+Zt29HxmaBUaW17+2VljrFYKlWKiNSZvJq3red9J5TkrrHl3TWgGJpVKSJSR/Ju3rZgrOd9L5TkbrCe11DqQCOiWZUiIjWu6J23bXv7Jf1JzvOW2dbWCSWIM3J7jxnzO1SqlCJUS8lCpB6NAn4GeMH5EuBMYEO+b2Q970vAFUADsJpEwjOLF/8hqkCjZM84Y3s2b772rZ6eMyffdRdvbNoEcDswPebQpMpUy+wqkXrTDDyAS25J4OLgOO/kBmB8/yrgE7ieud1IJu+3nvdtO23ayGjCjYZtb5/Kli1/wpgzxw0bxiWTJz8cPKVZlZI3XcGJVJ4WwMf1t63DfbH/Koo3tqeeuhsNDZ3AkcFDL2LMXNPZ+Zso3r/guDxvX+A7wInBQ+8AXzC+fyNuVuVMYC1uos1rccQo1UcJTqSyzAWuxk39fxE4BXgyyg8IJprMBb4JjAke/j1wifH9O6P8rBxi2Qdrv4AxZ+P+my3GdGHtfxjffyUYNg54CpiISpWSByU4kcrQBFxHeur/MqAD1/xcEsHV3DXAqaGHHwW+z7BhN5sFC9aV5HPPOaeJtWtbsfZzuKvV1PfQQ8CFxvcfyvCyaaRbBmYBC0oRm9QWJTiR+E3Arf5/bHB+LXAh0FuOD7czZhxGMvk14CTS3wkbMeZWkkkfY5Yb33+7qM+YPXsUmzZNxdqTMeZTwNjQ0w9h7ZV0dd1i3KzJwahUKXlRghOJ12TgVuD9wBbceozXxxGIbWs7mETii7ieu9Ghp5K4MulvgacxZhV9fat4661XzPLl/UnYtrQ0suuu40gmd8La8SSTkzHmQCD1E14XcyPWLqKh4ftm8eLHcwxRpUrJixKcSHxagV/gksnfgXbcvbBY2WnTRrLddidj7enA8aTv0xVrHXAH1i7FmDuM779TwHuoVCk5U4ITKb8EcClwEe7f4GO4ySSr4wwqE9vS0sj48QcCx2DMEVi7F/BBYIchXtoLPIe1TwArSCQex9oHjO9viSAslSolJ0pwIuUVWfN2nKznjSeZ3I1EIt1Lm0wmsfZtttuuu1QTVAIqVYqIVJhmgp23gT7gy+iXzEJprUoRkQrRQmjnbdyMRSmOttUREYnZXKAH92W8Cjgg3nBqhrbVERGJSWrn7VQp7V7cl7JER6VKEZEyy2nnbYmESpUiImWS187bUjSVKiUjzeASiVZFNm8Pxnreara+6jFmtuns/OU2Y9vbr8KYLwL30Ng40yxa9I8yhZkLNYDLNrQfnEg0UjtvL8Elt8eAQ6ng5Bb4NS7me0KPnZhxZF/fJcArwMfo7b3fet7ojOPicTuwKDi+DpUqBSU4kSiMAm4i3de2BLfEVcWtTLI14/vnGt9vxzVLbwLA2k/YDNUdc8stb2HtpcHpJIz5bPkizcn5wBvAjsAPYo5FKoASnEhxmolw5+24GN/fiFtMGWA8bW2HZByYTKb3i7O2tfSR5eUt0vc7tQO4KMGJFKEFeAS3Uv464GTgcrJv+VK5rE0nL2Mylyl33vn10NnEEkdUCJUqpZ8SnEhh5gJ3Azvjdt4+FvhVrBEVK5cE190d3lng2RJHVCiVKgVQghPJV6p5+3u4vrZlwGG4/dKqmlmy5FngpeB0ivW8bXcMsPbg0HGlTslXqVIAJTiRfEzArUaS+vK8Fvgk7gu1NqSv4hqBj2/zfCLREhytZ8uWxeUJqiAqVYoSnEiOJgMP4UqRW4BzgQtw+57VkjtDxwPKlHbevATW/mtw+kNz223ryxdWQVSqrHNKcCJDa8Ult/fjmrc/Clwfa0SlYsy9uAQO7uo0beXKk4A9gG4aG68oc2SFUKmyzinBiQyuWpu3C2Z8/5+4tgeA3eyMGZMBgr64bwaPX1xhq5hko1JlHVOCE8msapu3ixaeTWmtK1N63izcNj/34/s/jiewgqlUWaeU4ES21UwNNG8XzJg7+o+tPdG2to4DvgNsJJk821Rfn59KlXVKiy2LDNQC+Lj+tnW4L8Pq7m8rQGgR5i24Ml8bcKHx/atiDaw4C4GZwFrcpKHX4g1HSk1XcCJptde8XShr7wqOhuGS24Pst993Y4woCipV1hklOCmcZ1fjWbvVz7fjDqsANdu8XbBwmdKVJueYefOSscUTDZUq64wSnBRmjh2B5T4MC4A/9T9ueTy+oApS+83bhejpuYf0vbYnzJIlz8cZToQ0q7KOKMFJYW40m+gys+k0szChpGZ4Isao8lUvzdv5a2o6mvQ9+g/FGUoJqFRZJ5TgpHiWg4Kj9fj8NdZYclc/zduF+a/Q8U729NPHxhZJ9FSqrBNKcFKcc2wTsF9wtgJMpU8hr7vm7XzZtra9gCMGPNjTMy6eaEpGpco6oAQnxXmHfXEz7cBWfHmyfpu382HMMds8lkw2xhBJqalUWeOU4KQ46fIkJCp6gkkz9dy8nQ9jRm31iCWRWBNLLKWlUmWNq8XfyqS80gmujyfwbAOGWVjOwJUuxwF/x3IXSS7hZvNyDDG2oObt3CUSy0kmLelJJn8wvv92nCGVUKpUORNXqlxOuRrAT7O708ssDC3AvsB4oAH3d/QFEsxmsflLWWKpUbqCk+JYUhtgbqaJbmA5lhuBvYFu3NXSHhg+SwMr8OxBg7xTqah5O09m8eKngM8DbwIvkkx+LuaQSq28pcqZdhfa7Xz6WIXhUuADwMNYFgB/A3YCDqeHSt+OqOJpqS4pjme7cV8Mf8GV+1aR5CKWmFUATLdjGM7VwFnBK55jP/Zlnil103AT7jfyVAlqGdBBvfe3yWCmAakdymcBC0ryKe12atA7OhZ4gAT/wWLzh/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