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

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

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

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

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 

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 

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 

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 

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 

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 

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

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

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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