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2.5 Solving Right Triangles

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

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2.5 Solving Right Triangles

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

  2. 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 EX: Find sin (74 8 14)

  3. DEF:To solve a triangle SOHCAHTOA SinOh__ ___ Heck CosAnother =Hour TanOf___ Algebra

  4. B 12.7 a 34.5 A b C SOHCAHTOA 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 EX: Solve: A = 34 30

  5. B 17.4 a 28 C b A SOHCAHTOA 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 7)A = 28, c = 17.4 ft(23)

  6. B 387.1 a 53.4 C b A SOHCAHTOA 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  15) A = 53 24, c = 387.1 (31)

  7. M n p 51.2 P 124 N SOHCAHTOA 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 3)N =51.2

  8. A c 56.851 42.0892 B a C SOHCAHTOA 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 5)B =42.0892 (15)

  9. B 73 a c C 128 A SOHCAHTOA 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 9) B = 73, b = 128 in (25)

  10. B 29.43 53.58 C b A SOHCAHTOA 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 29.432 + b2 = 53.582 b2 = 2004.6915 b = 44.77 EX: Solve:

  11. B 76.4 c C 39.3 A SOHCAHTOA tan= Opp Adj tan A = 76.4 39.3 tan-1(76.4 39.3) = A 62.8 = A tan= Opp39.3 Adj 76.4 tan-1(39.3) = B 76.4 27.2 =B 76.42 + 39.32 = c2 c2 = 7381.45 c = 85.9 11) a = 76.4 yd, b = 39.3 yd (27)

  12. B a 7.813 C 2.467 A SOHCAHTOA 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 a2 + 2.4672 = 7.8132 a2 = 54.95688 a = 7.413 19) c = 7.813 m, b = 2.467 m

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