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

Answer 1

`color(brown)("Lengths of sides " a = b = 8.28`

Explanation:

`"Given : " hat A = pi/12, hat C = (pi)/6, hat B = pi - pi/12 - (5pi)/6 = pi/12, c = 15`

`"To find lengths a, b"`

Since `hat B = hat A`, it's an isosceles triangle with sides a & b equal.

Applying the law of sines,

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

`a = b = (16 * sin (pi/12)) / sin ((5pi)/6) = 32 sin (pi/12) = 8.28`