Chapter 6 – Trigonometric Functions: Right Triangle Approach 6.6 - Law of Cosines.

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Presentation transcript:

Chapter 6 – Trigonometric Functions: Right Triangle Approach Law of Cosines

Law of Cosines Like the Law of Sines, the Law of Cosines is also used for oblique triangles.

Law of Cosines We have two possible cases for the law of cosines.  Case 1 – Two sides and the included angle (SAS)  Case 2 – Three sides (SSS) Law of Sines

Definition Law of Cosines works when we have SAS or SSS.

Hint for Solving SAS

Solving Using SAS Solve the triangles shown below.

Hint for Solving SSS

Solving Using SSS Solve the triangle ABC if a = 8, b = 19, and c = 14.

Application Two airplanes leave an airport at the same time on different runways. One flies directly north at 400 mph. The other flies on a bearing of N75  E at 350 mph. How far apart will the airplanes be after two hours?

Heron’s Formula

Using Heron’s Formula Find the area of a triangle with a = 6 yards, b = 16 yards, and c = 18 yards.

Example – pg. 481 Find the area of the shaded figure, rounded to two decimals Law of Cosines

Examples – pg. 481 Find the indicated side x or angle . (Use either the Law of Sines or Law of Cosines, as appropriate.) Law of Cosines

More Examples – pg Law of Cosines

More Examples – pg Law of Cosines

More Examples – pg Law of Cosines

More Examples – pg Law of Cosines

More Examples – pg. 480 Solve triangle ABC Law of Cosines