Question

A triangle has sides A, B, and C. The angle between sides A and B is `(5pi)/12` and the angle between sides B and C is `pi/12`. If side B has a length of 36, what is the area of the triangle?

Answer 1

`:.color(brown)(A_t = (1/2) * a * c = (1/2) * 9.32 * 34.77 = 162.06 " sq units"`

Explanation:

`hat A = pi/12, hat C = (5pi)/12, hat B = pi - pi/12 - (5pi)/12 = pi/2, b = 36`

It's a right triangle with `hat B = 90^@`

As per the Law of Sines,

`color(purple)(a / sin A = b / sin B = c / sin C)`

`:. a = (b * sin A) / sin B = (36 * sin (pi/12)) / sin (pi/2) = 9.32`

`:. c = (b * sin C) / sin B = (36 * sin ((5pi)/12)) / sin (pi/2) = 34.77`

`:.color(brown)(A_t = (1/2) * a * c = (1/2) * 9.32 * 34.77 = 162.06 " sq units"`