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

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Presentation on theme: "2.5 Solving Right Triangles OBJ: Find missing sides and angles of a right triangle."— Presentation transcript:

1 2.5 Solving Right Triangles OBJ: Find missing sides and angles of a right triangle

2 EX:  Find sin (74  8 14  ) sin(74  8 14  ) sin( ) =  sin (  ) sin 0 0 sin 30.5 sin sin 90 1 sin sin (sin166).25 sin 180 0

3 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

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

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 sin(28  ) = a = a cos = Adj Hyp cos(28  ) = b cos(28  ) = b = b  B = 62 

6 15)  A = 53  24, c = (31) B a 53.4 Cb A SOH CAH TOA sin = Opp /60 = 53.4 Hyp sin(53.4) = a sin(53.4  ) = a = a cos = Adj Hyp cos(53.4  ) = b cos(53.4  ) = b = b  B = 36.6 

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

8 5)  B =  (15) A c  B a C SOH CAH TOA tan = Opp Adj tan(  ) = a /tan(  ) = a =a sin = Opp Hyp sin(  ) = c /sin(  ) = c = c  A = 

9 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 = a sin = Opp Hyp sin(73  ) = 128 c 128/sin(73  ) = c  a = 17 

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

11 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 = tan -1 ( ) =  A 62.8 =  A tan = Opp 39.3 Adj 76.4 tan -1 (39.3) =  B =  B = c 2 c 2 = c = 85.9

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


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