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Right Triangle Trigonometry (9.8)

Right Triangle Trigonometry (9.8). Trig Ratios ~ may only use with right triangles. S. C. T. o. h. a. h. o. a. osine. angent. ine. pposite. ypotenuse. djacent. ypotenuse. pposite. djacent. S. C. T. o. h. a. h. o. a. opposite side. Sin (Angle) =. hypotenuse.

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Right Triangle Trigonometry (9.8)

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  1. Right Triangle Trigonometry (9.8) Trig Ratios ~ may only use with right triangles

  2. S C T o h a h o a osine angent ine pposite ypotenuse djacent ypotenuse pposite djacent

  3. S C T o h a h o a opposite side Sin (Angle) = hypotenuse adjacent side Cos (Angle) = hypotenuse opposite side Tan (Angle) = adjacent side

  4. S C T o h a h o a A WRT  A: WRT  B: A hypotenuse opposite side hypotenuse c c b b adjacent side C B C B a a opposite side adjacent side a a b b Sin A = Tan A = Sin B = Tan B = c b c a b a Cos B = Cos A = c c

  5. A. Finding the values of a ratio: Example: a) Find the value of the sine ratio for A. A hypotenuse 14 10 adjacent B C 8 opposite opposite a 8 Sin A = =  0.5714 = c 14 hypotenuse

  6. Try at your seats: Example: b) Find the value of the cosine ratio for A. A hypotenuse 15 adjacent 10 C B opposite 8 adjacent b 10 cos A = =  0.6667 = c 15 hypotenuse

  7. B. Finding trig values using calculator: Example: Use a calculator. Round to the nearest four decimal places. a) Sin 45°  c) tan 86°  14.3007 .7071 b) cos 20°  .9397 45 20 86 sin enter cos enter tan enter NOTE: Make sure your calculator is in degree mode.

  8. tan enter • C. Using Trig Ratios to Find Sides: Need 1 angle (besides 90) and 1 side Example: Find the length of side BC. I. WRT A … A opposite hypotenuse Tan A = 60˚ 60 adjacent 15 x adjacent Tan 60˚ = 15 C B x opposite x (15) (15) 1.7321 = 15 25.9815 = x

  9. ~ Terms: Angle of depression line of sight Angle of elevation

  10. tan enter • Try at your seats: Example: A 62-foot tall tree is standing near a house. The angle of elevation from the base of the house to the tree top is 37. If the tree falls, will it hit the house? Toa 37 62 Tan 37˚ = hypotenuse x 62 feet 62 (x) (x) 0.7536 = opposite 37 x x = 82.3 ft x .7536(x) = 62 adjacent No, the tree will not hit the house if it falls. .7536 .7536

  11. 2nd • D. Finding angles using trig values and a calculator: Example: Use a calculator. Round angles to the nearest tenth. a) sin A 0.5299 c) tan x°  0.3482 b) cos C 0.7218 .5299 .3482 sin enter 2nd tan enter x = 19.2 You’re “undoing” sine A = 32.0 .7218 2nd cos enter C = 43.8 NOTE: Make sure your calculator is in degree mode.

  12. E. Using Trig Ratios to Find Angles: Example: Use a calculator. Round the angle to the nearest tenth. B Tangent, Sine, or Cosine? hypotenuse 29 29  43 opposite opposite Tangent x = adjacent x A C 29 43 Tangent x = adjacent 43 .6744 Tangent x = So, “undo” tangent x = 34.0 2nd tan .6744 enter

  13. Try at your seats: Example: Use a calculator. Round the angle to the nearest tenth. C adjacent Which trig function has opposite and hypotenuse? Tangent, Sine, or Cosine? opposite 12 x B 19 hypotenuse A Sin x = opposite hypotenuse Sin x = 12 19 Don’t Forget! “Undo” sine to figure out the angle: Sin x = .6316 x = 39.2 2nd Sin .6316 enter

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