Question

A triangle has sides A, B, and C. If the angle between sides A and B is `(pi)/12`, the angle between sides B and C is `(7pi)/12`, and the length of B is 17, what is the area of the triangle?

Answer 1

Area of triangle `color(green)(A_t = 139.57` sq units

Explanation:

`hat A = (7pi)/12, hat C = pi/12, hat B = pi/3, b = 17`

Applying Law of Sines, `a / sin A = b / sin B`

`a = (17 * sin ((7pi)/12) )/ sin (pi/3) = 18.96`

Area of triangle `A_t = (1/2) a b sin C`

`A_t = (1/2) * 18.96 * 17 * sin (pi/12) = 139.57` sq units