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Right Triangle Trigonometry

Right Triangle Trigonometry. 13.1 Day 1. What is Trigonometry?. Trigonometry is the study of how the sides and angles of a triangle are related to each other. It's all about triangles!. DEFINITIONS.

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Right Triangle Trigonometry

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  1. Right TriangleTrigonometry 13.1 Day 1

  2. What is Trigonometry? • Trigonometry is the study of how the sides and angles of a triangle are related to each other. • It's all about triangles!

  3. DEFINITIONS • Trigonometry: The study of the properties of triangles and trigonometric functions and their applications. • Trigonometric ratio: A ratio of the measures of two sides of a right triangle is called a trigonometric ratio.

  4. A Right Triangle Hypotenuse Opposite Adjacent

  5. Same Right Triangle – Different Angle B Hypotenuse Adjacent Opposite

  6. Right Triangle Trigonometry Right Triangle Definition of Trig Functions Let be an acute angle of a right triangle. opposite hypotenuse adjacent cos = adj hyp tan = opp adj sin = opp hyp cot = adj opp csc = hyp opp sec = hyp adj

  7. Remember SOH CAH TOA

  8. How the Trig Functions Relate to Each Other csc = 1 sin sin = 1 csc sec = 1 cos cos = 1 sec tan = 1 cot cot = 1 tan

  9. Example: Evaluate the six trigonometric functions of the angle shown. Use the Pythagorean Theorem to find the length of the adjacent side… a2 + 122=132 a2=25 a = 5 adj = 5 opp = 12 hyp = 13 13 12

  10. Example: Evaluate the six trigonometric functions of the angle shown. sin = opp hyp =12 13 13 12 cos = adj hyp = 5 13 5 = 13 5 tan = opp adj sec = hyp adj = 12 5 csc = hyp opp = 5 12 =13 12 cot = adj opp

  11. Example Find each value using a calculator. Round to the nearest thousandths. • cos 41º 3. sec 12º • sin 78º 4. cot 84º = .755 =1.022 = .978 = .105

  12. Find the missing parts of a triangle B 19º A =  B =  C = 71º c a 90º 19º C A 13 a = b= c = 13

  13. YOUR TURN Evaluate the six trigonometric functions of the angle ө shown. ө 13 5 12 Find all the missing parts of the triangle B 62º c 6 A C b

  14. angle of elevation– an angle formed by a horizontal line and the line of sight to an object above the level of the horizontal. angle of elevation

  15. angle of depression –an angle formed by a horizontal line and the line of sight to an object below the level of the horizontal. angle of depression

  16. A support cable from a radio tower makes an angle of 56º with the ground. If the cable is 250 feet long, how far above the ground does it meet the tower?

  17. You are standing at the end of the shadow of a giant sequoia tree, 150 feet from its base. The angle of elevation to the sun is 63º. How tall is the tree?

  18. The angle of depression from the top of the Smoke Town Lighthouse 120 ft above the surface of the water to a buoy is 10º. How far is the buoy from the base of lighthouse?

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