Question

A triangle has sides A, B, and C. The angle between sides A and B is `(pi)/4` and the angle between sides B and C is `pi/6`. If side B has a length of 8, what is the area of the triangle?

Answer 1

`color(green)(Delta " " A_t = (1/2) a b sin C = 11.71 " sq units"`

Explanation:

`hat A = pi/6, hat C = pi/4, b = 8`

`hat B = pi - pi/6 - pi/4 = (7pi)/12`

Applying the Law of Sines,

`a = (b sin A) / sin B = (8 * sin (pi/6) ) / sin ((7pi)/12) = 4.14 " units"`

`color(green)(Delta " " A_t = (1/2) a b sin C = (1/2) * 4.14 * 8 * sin (pi/4) = 11.71 " sq units"`