Concept Byte: Law of Sines and Law of Cosines

Use With Lesson 8-4

EXTENSION

You have seen sine and cosine defined in terms of acute angles in right triangles only. However, you can apply two special laws involving sines and cosines to any triangle. The Law of Sines lets you find missing measures in a triangle when you know the measures of two angles and the length of a side (AAS or ASA) or the lengths of two sides and the measure of a nonincluded angle (SSA). The Law of Cosines lets you find missing measures in a triangle when you know the lengths of two sides and the measure of the included angle (SAS) or the lengths of three sides (SSS).

For any Δ A B C cap delta eh b c with side lengths a, b, and c, each of the following is true.

Law of Sines		Law of Cosines
sin A a = sin B b = sin C c fraction sine eh , over eh end fraction . equals . fraction sine b , over b end fraction . equals . fraction sine c , over c end fraction		a 2 = b 2 + c 2 − 2 b c cos A b 2 = a 2 + c 2 − 2 a c cos B c 2 = a 2 + b 2 − 2 a b cos C table with 3 rows and 1 column , row1 column 1 , eh squared , equals , b squared , plus , c squared , minus 2 b c cosine eh , row2 column 1 , b squared , equals , eh squared , plus , c squared , minus 2 eh c cosine b , row3 column 1 , c squared , equals , eh squared , plus , b squared , minus 2 eh b cosine c , end table

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