Question

A triangle has sides A, B, and C. If the angle between sides A and B is `(5pi)/12`, the angle between sides B and C is `pi/3`, and the length of B is 2, what is the area of the triangle?

Answer 1

`A_t = (1/2) * 2.4495 * 2 * sin ((5pi)/12) = color (red)(2.366`

Explanation:

Given : `b = 2, hatA = pi/3, hatC = (5pi)/12`

`hatb = pi - (pi/3 + (5pi)/12) = pi/4`

`a / sin A = b / sin B = c / sin C`

`a = (b * sin A) / sin B = (2 * sin (pi/3)) / sin ((pi/4) = 2.4495`

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

`A_t = (1/2) * 2.4495 * 2 * sin ((5pi)/12) = color (red)(2.366`