Question

A triangle has sides A, B, and C. The angle between sides A and B is `(5pi)/12` and the angle between sides B and C is `pi/12`. If side B has a length of 23, what is the area of the triangle?

Answer 1

This is a right triangle with hypotenuse `B = 23`

Explanation:

The area is

`1/2(23sin(pi/12))(23cos(pi/12)) = 529/2 (sin(pi/12)cos(pi/12))`

`= 529/2(1/2sin((2pi)/12))`

`= 529/4(sin(pi/6))`

`= 529/8`