Question

A triangle has sides A, B, and C. The angle between sides A and B is `pi/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 triangle `Delta ABC = (1/2) a c sin B = color(blue)(0.134`

Explanation:

Given `hatC = pi/12, hatA = pi/12, b = 1`

It’s an isosceles triangle with sides a & c equal, as their angles are equal.

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

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

`a / sin ((pi)/12) = c / sin ((pi)/12) = 1/ sin ((5pi)/6)`

`a = c = (1 * sin (pi/12)) / sin ((5pi)/6) = 0.5176`

Area of triangle `Delta ABC = (1/2) a c sin B`

`=> (1/2) * 0.5176 * 0.5176 * sin ((5pi)/6) = color(blue)(0.134`