Question

A triangle has sides A, B, and C. The angle between sides A and B is `pi/3` and the angle between sides B and C is `pi/12`. If side B has a length of 7, what is the area of the triangle?

Answer 1

`A_t = (1/2) a b sin C = (1/2) * 1.8756 * 7 * sin (pi/3) = color(red)(5,6851)`

Explanation:

`b = 7, hatA = pi/12, hatC = pi/3`

`:. hatB = pi - pi/12 - pi/3 = (7pi)/12`

`a = (b * sin A) / sin B = (7 * sin (pi/12)) / sin ((7pi)/12) = 1.8756`

`A_t = (1/2) a b sin C = (1/2) * 1.8756 * 7 * sin (pi/3) = color(red)(5,6851)`