Question

A triangle has sides A, B, and C. The angle between sides A and B is `(5pi)/6`. If side C has a length of `14` and the angle between sides B and C is `pi/12`, what are the lengths of sides A and B?

Answer 1

Lengths of sides `color(brown)(a = b = 7.2469)`

Explanation:

To find the lengths of sides a, b.

Given `hatA = pi/12, hatC = (5pi)/6, c = 14`

Third angle `hat B = pi - pi/12 - (5pi)/6 = pi/12` by the law of sines.

As `hat B = hat C`, it’s an isosceles triangle, with sides a, b equal.

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

`a = b = (c * sin A) / sin C = (14 * sin (pi)/12) / sin ((5pi)/6) = color(brown)7.2469`