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1316 Trigonometry Law of Sines Chapter 7 Sections 1&2

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b a c B C A There is group of formulas that work for most triangles. h

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Requirements when using the Law of Sines: You must be given two angles and any side: AAS or ASA Two sides and an angle opposite one of them: SSA OR The Law of Sines does not work for SSS or SAS

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Find all sides and angles if C = 102.3°, B = 28.7°, and b = 27.4 feet. b a c B C A 102.3° 28.7° 27.4 ft 49.0°

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A pole tilts toward the sun at an angle of 8°. If it casts a 22 foot shadow and the angle of elevation from the tip of the shadow to the top of the pole is 43°, how tall is the pole? b a = ? c BC A 98° 43° = 22 ft 39° shadow

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When you are given two sides and a non-included angle (SSA) – three possibilities exist You will get no triangle You will get one triangle You will get two triangles a b a b a b a b

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Find all angles if A = 85°, a = 15, and b = 25 ft. b a c B C A 85° = 15 ft 25 ft This does not exist so there is no triangle.

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Find all angles if A = 20.5°, a = 12, and b = 31 feet. b a c B C A 20.5° = 12 ft 31 ft This happens twice on (0°,180°) 64.8 ° 94.7 ° 20.5° 44.3° 115.2°

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Use the Law of Sines to find B: 6 8 B C 87° A With Sine there may be an angle in Quad II that also works so you must check the supplement: This is too large to be a triangle with the 87 given

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Use the Law of Sines to find B: B C 60° A Check the supplement: The data makes two triangles since both 81.8 & 98.2 work with 60

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Use the Law of Sines to find C: B C 67° A No triangle will be formed with these numbers.

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Draw a triangle for each and use the Law of Sines to decide how many triangles are formed 1) B = 47°, b = 4, c = 25 No Triangle 2) C = 60°, b = 30, c = 50 One Triangle 3) B = 20°, a = 12, b = 5 Two triangles 4) B = 37.3°, b = 12.5, c = 20.1 Two triangles 5) A = 102°, a = 5, c = 12 No triangles

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Basic Steps for working with Law of Sines Use Law of Sines with the parts you are given Draw and label a figure When you find an angle (Sin -1 ) check if the supplement also makes a triangle Find all missing parts that are requested.

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