Chapter 8 Section 8.2 Law of Cosines. In any triangle (not necessarily a right triangle) the square of the length of one side of the triangle is equal.

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Presentation transcript:

Chapter 8 Section 8.2 Law of Cosines

In any triangle (not necessarily a right triangle) the square of the length of one side of the triangle is equal to the sum of the squares of the two remaining sides minus twice the product of the cosine of the angle of the opposite side and the lengths of the two sides forming the angle. It is like the "Pythagorean Theorem" for any triangle. B A c b a C The Law of Cosines enables you to solve the triangle in the cases where your know all 3 sides (SSS) or 2 sides and the included angle (SAS) A B C

9 10 a B C Example: Find the remaining sides and angles of the triangle pictured to the right (SAS). To find a, apply the Law of Cosines: To find C, apply the Law of Sines: Subtract o find angle B : In this case we do not need to worry about another angle C since this (SAS) always determines a unique triangle. So now, given 3 sides, or a pair of sides and an angle, or a pair of angles and a side you can now determine all possible triangles.

Draw a picture. Airport To find a, apply the Law of Cosines: a B To find B, apply the Law of Sines: