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In the last lesson we used the Law of Cosines to find the length of the third side of a triangle when you know the length of two sides and the angle in between. This law can also be used to find the measure of an angle when the three sides of a triangle are given. To use the Law of Cosines to find an unknown angle: 1. Identify c as the side across from the angle you are trying to find. 2. Substitute the values into the Law of Cosines.
Knowing only the lengths of two sides of the triangle, and no angles, you cannot calculate the length of the third side; there are an infinite number of answers. To illustrate, imagine that you have two fixed-length pieces of wood, and you drill a hole near the end of each one and put a nail through the hole.