Question

A triangle has sides A, B, and C. The angle between sides A and B is `(3pi)/4`. If side C has a length of `24` 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(red)(a = 8.7846, b = 16.9706`

Explanation:

Given : `hatA = pi/12, hat C = (3pi)/4, c = 24`

To find `a, b`

Third angle `hat B = pi - (3pi)/4 - pi/12 = pi/6`

By the law of sines,

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

`a = (c * sin A) / sin C = (24 * sin (pi/12)) / sin ((3pi)/4) = color(purple)(8.7846)`

`b = (c * sin B) / sin C = (24 * sin (pi/6)) / sin ((3pi)/4) = color (purple)(16.9706`