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2.5 Solving Right Triangles OBJ: Find missing sides and angles of a right triangle

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EX: Find sin (74 8 14 ) sin(74 8 14 ) sin(74 + 8 60 + 14 3600) =.962 74.137 sin (74.137 ) sin 0 0 sin 30.5 sin 60.87 sin 90 1 sin 120.87 sin 150.5 (sin166).25 sin 180 0

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DEF: To solve a triangle SOH CAH TOA Sin Oh__ ___ Heck Cos Another = Hour Tan Of___ Algebra SinOpp Hyp CscHyp Opp CosAdj Hyp SecHyp Adj TanOpp Adj CotAdj Opp

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EX: Solve: A = 34 30 B 12.7 a 34.5 Ab C SOH CAH TOA sin = Opp Hyp sin(34.5 ) = a 12.7 12.7 sin(34.5 ) = a 7.193 = a cos = Adj Hyp cos(34.5 ) = b 12.7 12.7 cos(34.5 ) = b 10.466 = b B = 55.5

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7) A = 28 , c = 17.4 ft (23) B 17.4 a 28 Cb A SOH CAH TOA sin = Opp Hyp sin(28 ) = a 17.4 17.4 sin(28 ) = a 8.169 = a cos = Adj Hyp cos(28 ) = b 17.4 17.4 cos(28 ) = b 15.363 = b B = 62

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15) A = 53 24, c = 387.1 (31) B 387.1 a 53.4 Cb A SOH CAH TOA sin = Opp 53 + 24/60 = 53.4 Hyp sin(53.4) = a 387.1 387.1 sin(53.4 ) = a 310.771= a cos = Adj Hyp cos(53.4 ) = b 387.1 387.1 cos(53.4 ) = b 230.799= b B = 36.6

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3) N =51.2 M n p 51.2 P 124 N SOH CAH TOA tan = Opp Adj tan(51.2 ) = n 124 124 tan(51.2 ) = n 154.225 = n cos = Adj Hyp cos(51.2 ) = 124 p 124/cos(51.2 ) = p 197.892 = p M = 38.8

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5) B =42.0892 (15) A c 56.851 42.0892 B a C SOH CAH TOA tan = Opp Adj tan(42.0892 ) = 56.851 a 56.851/tan(42.0892 ) = a 62.942 =a sin = Opp Hyp sin(42.0892 ) = 56.851 c 56.851/sin(42.0892 ) = c 84.816 = c A = 47.9108

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9) B = 73 , b = 128 in (25) B 73 a c C 128 A SOH CAH TOA tan = Opp Adj tan(73 ) = 128 a 128/tan(73 ) = a 39.134 = a sin = Opp Hyp sin(73 ) = 128 c 128/sin(73 ) = c 133.849 a = 17

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EX: Solve: B 29.43 53.58 C bA SOH CAH TOA sin = Opp Hyp sin A = 29.43 53.58 sin -1 (29.43/53.58) = A 33.3 = A cos = Adj Hyp cos -1 (29.43/53.58) = B 56.7 29.43 2 + b 2 = 53.58 2 b 2 = 2004.6915 b = 44.77

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11) a = 76.4 yd, b = 39.3 yd (27) B 76.4 c C 39.3A SOH CAH TOA tan = Opp Adj tan A = 76.4 39.3 tan -1 (76.4 39.3) = A 62.8 = A tan = Opp 39.3 Adj 76.4 tan -1 (39.3) = B 76.4 27.2 = B 76.4 2 + 39.3 2 = c 2 c 2 = 7381.45 c = 85.9

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19) c = 7.813 m, b = 2.467 m B a 7.813 C 2.467 A SOH CAH TOA cos = Adj Hyp cos A = 2.467 7.813 cos -1 (2.467/7.813) = A 71.6 = A sin = Opp = 2.467 Hyp 7.813 sin -1 (2.467/7.813) = B 18.4 = B a 2 + 2.467 2 = 7.813 2 a 2 = 54.95688 a = 7.413

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