Question

A triangle has sides A,B, and C. If the angle between sides A and B is `(2pi)/3`, the angle between sides B and C is `pi/4`, and the length of B is 13, what is the area of the triangle?

Answer 1

(169 `sqrt`6 / 8) cosec (`pi/12`) = 200, areal units, nearly

Explanation:

Using lower case letters a, b and c for angles and a + b + c = `pi`,
.with a = `pi/4` and c = `2pi/3` , b = `pi/12`.
Using B/sin(b) = A/sin(a), A = 13 sin(`pi/4`) / sin (`pi/12`)
Using, area = base X altitude / 2, the answer is B X A X sin (c) / 2.