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1. 12.3 The Law of Sines

   C Find the area of ∆ABC 100 m First, find the height of the triangle The law of sines is related to the area of a triangle sin 40⁰ = CD/100 CD = (100) sin 40⁰ 40⁰ A B D Now find the area. 150 m A = (.5) b h A = (0.5)(150)(100 sin 40⁰ A ≈ 4821 m2
2. Investigation 1: Area of a Triangle p.634 SAS Triangle Area Conjecture The area of a triangle is given by the formula A = _____________ where a and b are the lengths of two sides and C is the angle between them. (0.5) ab sin C Deductive reasoning Investigation 2: The Law of Sines Step 1: __________________ Step 2: __________________ Step 3: _______________ _______________ __________________ Step 4: __________________ Step 5: __________________ Step 6: _______________ _______________ __________________ h = a sin B h = b sin A b sin A = a sin B abab sin A = sin B a b b sin A = a sin b k = c sin B k = b sin C c sin B = b sin C cbcb sin B = sin C b c c sin B = b sin C Law of Sines For a triangle with angles A, B, and C and sides of lengths a, b, and c (a opposite A, b opposite B, and c opposite C), sin A = __________ = ___________ b sin B sin C c a