Question

Find x. Round to the nearest degree.

Answer 1

The Law of Cosines features the 3 side lengths of a triangle, plus the measure of the angle opposite one of those sides.

We want angle x, which is opposite the side of length 39.

Then: a^2 = b^2 - 2ab cos C becomes 39^2 = 36^2 + 59^2 - 2(36)(59)cos x

or 1521 = 3481 + 1296 - 2(36)(59) cos x

Subtract (3481+1296) from both sides: 1521 - 4777 = -4248cos x

-3256 = -4248cos x

-3256

Then: cosx = --------------- = 0.766

-4248

Solving for x: x = arccos -0.766 = 0.698 radian, or 40 degrees (answer)