Question

A triangle has sides A, B, and C. The angle between sides A and B is `pi/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

`color(magenta)("Area of Triangle " A_t = 1.183`

Explanation:

`hat A = pi/12, hat C = pi/4, hat B = (2pi)/3, b = 1`

As per Law of sines,

`a = (b * sin A) / sin B = (1 * sin ((2pi)/3)) / sin (pi/12)`

`a = 3.346`

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

`A_t = (1/2) * 3.346 * 1 * sin (pi/4) = 1.183`