A piece of wire is bent into the shape of a triangle. Two sides have length 22 inches and 20 inches. The angle between these two sides is 55°.

Question

What is the length of the third side to the nearest hundredth of an inch?

The length of third side is approximately  __?__ inches

Answer 1

we use cosine rule to find the 3rd side:

Let the third side be C, then

C^2 = 22^2 + 20^2 - 2x22x20cos(55) = 27,295

C = sqrt(27295) = 418 inches

Answer 2

You are given the lengths of 2 sides and the measure of the angle between those 2 sides.

Use the law of cosines:

c^2 = a^2 + b^2 - 2abcosC