Question

A triangle has sides A, B, and C. The angle between sides A and B is `(3pi)/4` and the angle between sides B and C is `pi/12`. If side B has a length of 1, what is the area of the triangle?

Answer 1

Area of `Delta` `A_t = (1/2) a b sin C = 0.183`

Explanation:

`b = 1, hatA = pi/12, hatC = (3pi)/4`

`hat B = pi - pi/12 - (3pi)/4 = pi/6`

`a / sin A = b / sin B`

`a = ((1 * sin (pi/12)) / sin (pi/6) = 0.5176`

Area of `Delta` `A_t = (1/2) a b sin C`

`A_t = (1/2) 0.5176 * 1 sin ((3pi)/4) = 0.183`