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 1, what is the area of the triangle?

Answer 1

Area of right `Delta ABC = color(green)(0.125`

Explanation:

Given `hatA = pi/12, b = 1, hat C = (5pi)/13`

Third angle `hat B = pi - (5pu)/12 - pi / 12 = pi/2`

Hence it’s a right triangle.

`a / sin A = b / sin B = c / sin C`

`a / sin (pi/12) = 1 / sin (pi/2) = c / sin ((5pi)/12) = 1`, since `sin (pi/2) = 1`

`a = sin (pi/12) = 0.2588`

`c = sin ((5pi)/12) = 0.9659`

Area of right `Delta ABC = (1/2) a c = (1/2) * 0.2588 * 0.9659 = color(green)(0.125`