The goal of this page is to help students better understand when to use the law of sines and when to use the Law of Cosines
Triangle 1 and 2 are clear candidates for the law of sines
Triangle 1 (Top left)
- Law of Sines
Triangle 2 (Top Left)
Triangle 3( Bottom Left)
To get the measure of x . You wold first need to use the law of cosines to get the length of the side opposite the 115° triangle. From there you could use the law of sines
Triangle 4( Bottom Right)
Since the sum of the measure of the interior angles of a triangle is 180°, you can find the measure of the 3rd angle . From there you could use the law of sines to calculate the length of side x.
Since you know 3 sides, and are trying to find an angle this is Law of Cosines problem.
8² = 5² + 6² -2(5)(6)(cos(x))
Since you know 2 sides , their included angle, and you are trying to find the side length opposite the angle, this is Law of Cosines problem.
x² = 11² + 7² -2(11)(7)(cos(50))
Since you know a side length (11) and its opposite angle (50) and want to the angle measurement opposite the length of side 7, this is a law of sines problem