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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.
To find the missing angle, we can either use the formula and a bit of algebra or simply subtract the two known angles from 180 to find the unknown third. Let's see how this works. We have a triangle here for which we know two of the angles. We see that the two angles measure 49 and 28 degrees, respectively. To find the third, we can plug these values into our formula. Because it doesn't matter how we label our angles, we will just call the 49 degree angle a and the 28 degree angle b. So our formula becomes 49 + 28 + c = 180.