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7.1 Law of Sines Day 1 Do Now Let Triangle ABC be a right triangle where angle C is 90 degrees, angle B is 37.1 degrees, and side BC is 6.3 Solve the triangle

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Test Review Retakes by

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Solving Triangles To solve a triangle means to find the lengths of all its sides and the measures of all its angles Weve solved right triangles previously

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Oblique Triangles A triangle that is not a right triangle is considered oblique Oblique triangles can be solved if at least one side and any other 2 measures (length or angle) are known

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Law of Sines Proof

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Law of Sines In any triangle ABC, Where side a is opposite of angle A, etc

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Law of Sines notes When solving triangles, there is a possibility that you can have one solution, two solutions, or no solution. This depends on the equations you set up – Remember, the range of sinx is [-1, 1]

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Ex1 In triangle EFG, e = 4.56, E = 43deg, G = 57 deg Solve the triangle

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Ex3 In Triangle QRS, q = 15, r = 28, Q = 43.6 deg Solve the triangle

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Ex 4 In triangle XYZ, x = 23.5, y = 9.8, X = 39.7 deg Solve the triangle

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Ex5 In triangle ABC, b = 15, c = 20, B = 29 deg Solve the triangle

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Closure Solve the triangle ABC, if possible A = 131 deg, C = 23 deg, b = 10 HW: p.608 #1-15 odds

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7.1 Law of Sines Day 2 Do Now In triangle ABC, B = 115deg, c = 45.6 yd, b = 23.8 yd. Solve the triangle

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HW Review: p.608 #1-15

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Ex2 In book

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Area of a Triangle Using the law of sines, we can find the area K of a triangle

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Ex6 A university landscaping architecture department is designing a garden for a triangular area in a dormitory complex. Two sides of the garden, formed by the sidewalks in front of buildings A and B, measure 172 ft and 186 ft respectively, and together form a 53 degree angle. The third side of the garden measures 160 ft. Find the area of the garden to the nearest square foot.

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Closure Find the area of the triangle ABC given C = 75.16 degrees, a = 1.5 m, b = 2.1 m HW: p.608 #17-31 odds

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