Question

A triangle has sides A, B, and C. The angle between sides A and B is `(pi)/6`. If side C has a length of `2` and the angle between sides B and C is `(7pi)/12`, what are the lengths of sides A and B?

Answer 1

`color(brown)(a = 3.86, b = 2.828`

Explanation:

`hat A = (7pi)/12, hat C = pi/6, hat B = pi - (7pi)/12 - pi/6 = pi/4, c = 2`

Applying the law of sines,

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

`a = (c * sin A) / sin C = (2 * sin ((7pi)/12))/ sin (pi/6) = 3.86`

`b = (c * sin B) / sin C = (2 * sin (pi/4)) / sin (pi/6) = 2.828`