Section 6.2 The Law of Cosines

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Presentation transcript:

Section 6.2 The Law of Cosines

Warm Up 6.2 1) Why can't the law of sines be used to determine the measures of the missing angles and/or sides? The law of sines CANNOT be used to determine the measures of missing angles and sides of triangles when the measures of two sides and an included angle (SAS) or the measures of three sides (SSS) are known. Since the law of sines can only be used in certain situations, we need to develop another method to address the other possible cases. This new method is called the law of cosines Are there unique triangles with the side and angle measures given above? Why? [Yes. SSS and SAS are two methods that prove triangles congruent. Therefore, if three sides of a triangle are known, or if two sides and an included angle are known, the triangle is unique.] Why can't the law of sines be used to determine the measures of the missing angles and/or sides? [To use the law of sines, you need to know the measure of at least one angle in the triangle. In addition, you need to know the measure of an angle and an opposite side to use the law of sines. Since that information is not given, the law of sines cannot be used.]

You Try! Solve for the missing angles in the SSS triangle a = 8ft b= 19ft c=14ft

The Law of Sines is used when we are given: Two angles and a side (AAS or ASA); two sides and a non-included angle (SSA). Law of Cosines is used when we are given: Three sides (SSS); two sides and an included angle (SAS).

EX 2: Solving an SAS triangle

You Try!

EX 3: