Question

A triangle has sides A, B, and C. The angle between sides A and B is `(5pi)/6` and the angle between sides B and C is `pi/12`. If side B has a length of 6, what is the area of the triangle?

Answer 1

Area `A_t =/(1/2) 6 * 6 * sin ((5pi)/6) = color(red)(9`

Explanation:

`hatA = pi/12, hatC = (5pi)/6, b = 6`

`hatB = pi - (5pi)/6 - pi/12 = pi/12`

`hatA = hatB, :. a = b = 6` (isosceles triangle)

Area `A_t =/(1/2) 6 * 6 * sin ((5pi)/6) = color(red)(9`