Symbolically Solving a multi-variable system of three equations for three variables

How can I find symbolic solutions for a,b, and c expressing them with respect to the other variables using the system of equations

(-2Nsinθ)/3=mL(b)

c=-(5bLcosθ)/6+(5(a^2)Lsinθ)/6

N=m( (5bLsinθ)/6+(5(a^2)L)/6cosθ +3g)

Answer 1

[Ameer Hamza]

Try this

syms a b c N theta m L b g

eq1 = (-2*N*sin(theta))/3==m*L*b;
eq2 = c == -(5*b*L*cos(theta))/6+(5*(a^2)*L*sin(theta))/6;
eq3 = N == m*((5*b*L*sin(theta))/6+(5*(a^2)*L)/6*cos(theta)+3*g);

sol = solve([eq1 eq2 eq3], [a b c]);

Result:

>> sol.a
ans =
 -((8*(9*N - 27*g*m + 5*N*sin(theta)^2))/(15*L*m*cos(theta)))^(1/2)/2
  ((8*(9*N - 27*g*m + 5*N*sin(theta)^2))/(15*L*m*cos(theta)))^(1/2)/2
 
>> sol.b
ans =
 -(2*N*sin(theta))/(3*L*m)
 -(2*N*sin(theta))/(3*L*m)
 
>> sol.c
ans =
 (sin(theta)*(9*N - 27*g*m + 5*N*cos(theta)^2 + 5*N*sin(theta)^2))/(9*m*cos(theta))
 (sin(theta)*(9*N - 27*g*m + 5*N*cos(theta)^2 + 5*N*sin(theta)^2))/(9*m*cos(theta))

[Aleem Andrew]

Thank you