Triangle Area in sine

Question

The perimeter of a triangle ABC is L metres. Find the area of the triangle in terms of L and the triangle’s angles α, β and γ.

(Let AB=x. Using the sine rule, first find the other side lengths in terms of x.)

Answer 1

Answer 2

A on the left, B at top, C on the right.

Drops perpendicular height from B to AC.

Area = 1/2 * h * b

sin A = h/x

h = x*sin A

cos A = b/x

b = x*cos A

Area = 1/2 * (x*sinA)*(x*cosA)

= 1/2 * x^2 * sin A * cos A