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Chapter 6 – Trigonometric Functions: Right Triangle Approach 6.6 - Law of Cosines
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Law of Cosines Like the Law of Sines, the Law of Cosines is also used for oblique triangles.
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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) 6.5 - Law of Sines
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Definition Law of Cosines works when we have SAS or SSS.
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Hint for Solving SAS
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Solving Using SAS Solve the triangles shown below.
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Hint for Solving SSS
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Solving Using SSS Solve the triangle ABC if a = 8, b = 19, and c = 14.
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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?
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Heron’s Formula
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Using Heron’s Formula Find the area of a triangle with a = 6 yards, b = 16 yards, and c = 18 yards.
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Example – pg. 481 Find the area of the shaded figure, rounded to two decimals. 6.6 - Law of Cosines
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Examples – pg. 481 Find the indicated side x or angle . (Use either the Law of Sines or Law of Cosines, as appropriate.) 6.6 - Law of Cosines
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More Examples – pg. 481 6.6 - Law of Cosines
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More Examples – pg. 482 6.6 - Law of Cosines
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More Examples – pg. 482 6.6 - Law of Cosines
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More Examples – pg. 482 6.6 - Law of Cosines
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More Examples – pg. 480 Solve triangle ABC. 6.6 - Law of Cosines
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