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 `35` and the angle between sides B and C is `pi/12`, what are the lengths of sides A and B?

Answer 1

`color(purple)("Lengths of sides " a = b = 18.12 " units"`

Explanation:

`hat C = (5pi)/6, hat A = pi/12, c = 35`

`hat B = pi - (5pi)/6 - pi/12 = pi/12`

It's an isosceles triangle with sides a & b equal.

Applying Law of Sines,

`a = b = (c * sin A) / sin C = (35 * sin (pi/12)) / sin ((5pi)/6) = 18.12 "units"`