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Essential Question: What is the law of sines, and how to we apply it?

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10-2: The Law of Sines For these next two sections, you will need to be in degree mode In any triangle ABC (in standard notation), the law of sines states (Proof on board)

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10-2: The Law of Sines Solve a Triangle with AAS Information Example 1: If B = 20 °, C = 31 ° and b = 210, find the other angle measure and side lengths. Sometimes it helps if you draw a triangle Label it Finding A should be obvious Use the law of sines to find the side lengths (next slide) A B C 20 ° 31 ° 210 129 °

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10-2: The Law of Sines Solve a Triangle with AAS Information Use the law of sines to find the side lengths A B C 20 ° 31 ° 210 129 °

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10-2: The Law of Sines The ambiguous case When dealing with an AAS triangle, theres only one solution – that goes back to your rules about triangle similarity (the same is true when given ASA and SAS) However, when dealing with a triangle with SSA (or ASS) information, were left with some unknowns… ? A

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10-2: The Law of Sines Solving a Triangle with SSA Information (no solution) Example 2: Given a possible triangle ABC with a = 6, b = 7 and A = 65 °, find angle B. Use the law of sines Because the maximum of a sine function is 1, there is no B possible, and there is no triangle possible.

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10-2: The Law of Sines Solving a Triangle with SSA Information (one solution) Example 3: An airplane A takes off from carrier B and flies in a straight line for 12 km. At that instant, an observer on destroyer C, located 5 km from the carrier, notes that the angle determined by the carrier, the destroyer (vertex) and the plane is 37 °. How far is the plane from the destroyer? A B C 37 ° 5 12 (not possible)

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10-2: The Law of Sines Solving a Triangle with SSA Information (one solution) Example 4:Solve triangle ABC when a = 7.5, b = 12, and A = 35 °. (continued next slide) A B C 35 ° 7.5 12

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10-2: The Law of Sines Solving a Triangle with SSA Information (one solution) Example 4:Solve triangle ABC when a = 7.5, b = 12, and A = 35 °. Case 1: B = 66.6 ° Case 2: B = 113.4 ° C = 180 – 66.6 = 78.4 ° C = 180 – 113.4 = 31.6 °

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10-2: The Law of Sines Assignment Page 634 1 – 7 17 – 25 33 – 35 odd problems Show work

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Essential Question: What is the law of sines, and how to we apply it?

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