Question

A triangle has sides A, B, and C. If the angle between sides A and B is `(3pi)/8`, the angle between sides B and C is `(pi)/3`, and the length of B is 6, what is the area of the triangle?

Answer 1

`color(crimson)(A_t = (1/2) a b sin C ~~ 18.55 " sq units"`

Explanation:

`hat A = pi/3, hat C = (3pi)/8, hat C = pi - pi/3 - (3pi) / 8 = (7pi) / 24, b = 6`

Applying the Law of Sines,

`a = (b sin A) / sin B = (6 * sin (pi/3)) / sin ((7pi)/24) ~~ 6.55`

Formula for area of triangle is `A_t = (1/2) a b sin C`

`color(crimson)(A_t = (1/2) 6.55 * 6 * sin ((3pi) / 8) ~~ 18.55 " sq units"`