Section 9.3 The Law of Cosines. THE LAW OF COSINES c a b α β γ.

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Presentation transcript:

Section 9.3 The Law of Cosines

THE LAW OF COSINES c a b α β γ

WHEN TO USE THE LAW OF COSINES (a)a side-angle-side (SAS) triangle or (b)a side-side-side (SSS) triangle. The Law of Cosines is used when you have:

TIPS ON USING THE LAW OF COSINES Since the Law of Cosines is more complicated than the Law of Sines, we usually use it only once and then use the Law of Sines. If we have a SSS triangle, we use the Law of Cosines to solve for the largest angle. This eliminates the ambiguous case when we use the Law of Sines.

EXAMPLE A ship leaves Norfolk at noon with a heading of 41° at a constant speed of 12 mph. At 5:30 pm, the course is changed to a heading of 100° to avoid a storm. At midnight, find the distance and bearing from Norfolk.