Question

A triangle has sides A, B, and C. The angle between sides A and B is `(7pi)/12` and the angle between sides B and C is `pi/12`. If side B has a length of 19, what is the area of the triangle?

Answer 1

`a = (1/2) a b sin C ~~ color(purple)(5.6783`

Explanation:

`hatC = (7pi)/12, hatA = pi/12, b = 19`

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

`a / sin A = b / sin B`

`a = (1/2) a b sin C = (19 * sin (pi/12)) / sin(pi/3) ~~ color(purple)(5.6783`