Question

A triangle has sides A, B, and C. If the angle between sides A and B is `(pi)/8`, the angle between sides B and C is `(7pi)/12`, and the length of B is 12, what is the area of the triangle?

Answer 1

Area of triangle

`A_t = (1/2) a b sin C = 33.5467`

Explanation:

`hatA = (7pi)/12, hatC = (pi)/8, b = 12`

`hatB = pi - (7pi)/12 - pi/8 = (7pi)/24`

`a = (12 * sin ((7pi)/12)) / sin((7pi)/24) = 14.6103`

Area of triangle

`A_t = (1/2) a b sin C = (1/2) * 14.6103 * 12 * sin (pi/8) = 33.5467`