Trigonometry : Law of Cosines
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Example Question #63 : Triangles
If 
Since we are give the length of two sides of a triangle and the corresponding angle of the third side, we can use the Law of Cosines to find the length of the third side. Because we are looking for 
Taking the square root of both sides we isolate
Substituting in the values from the problem gives
Example Question #61 : Triangles
If 
Because the problem gives the length of two of the three sides of a triangle and the corresponding angle of the third side, we can use the Law of Cosines to find the length of the third side. This gives use the equation
We can take the square root of both sides in order to give the equation
Substituting in the values given from the problem gives
Example Question #321 : Trigonometry
Suppose there was a triangle with side lengths 8,7, 14. What is the measure of the largest angle, rounded to the nearest degree?
The largest angle will be opposite the largest of the three side lengths, 14. We can find its measure using the law of cosines:
From here take the inverse cosine of each side to find the degress value that is angle C.
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