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Goal : To use trigonometric ratios for indirect measurements of right triangles.

7.6 Apply Sine and Cosine Ratios. Goal : To use trigonometric ratios for indirect measurements of right triangles. Trigonometry. Derived from Greek words, “trigonon" which means triangle, and "metria” which means measure. Trigonon metria = “triangle measurement”.

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Goal : To use trigonometric ratios for indirect measurements of right triangles.

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  1. 7.6 Apply Sine and Cosine Ratios Goal: To use trigonometric ratios for indirect measurements of right triangles.

  2. Trigonometry Derived from Greek words, “trigonon" which means triangle, and "metria” which means measure. Trigonon metria = “triangle measurement” • Sine - comes from the Latin word sinus meaning a curve or fold. • Cosine - was originally written "co.sine," short for COMPLEMENTI SINUS: the sine of the complementary angle. • Tangent - comes from the Latin word tangens which is a straight line which touches a circle at one point.

  3. Triangle Ratios

  4. SOH CAH TOAis mnemonic for: SOH CAH TOA

  5. Trigonometry B c a C A b

  6. Example 3 -HOTSThink….Ink….Share

  7. Example 3 Solutions

  8. Angle of Depression 42 ° 42 ° Angle of Elevation

  9. Example 4 – hots Finding a Hypotenuse using an angle of depression

  10. Example 4 solution

  11. You want to build a skateboard ramp with a length of 14 feet and an angle of elevation of 26°. You need to find the height and length of the base of the ramp. cos26o = sin26o = cos26o x y = = adj. hyp. opp. hyp. sin26o 14 14 14 cos 26o = y 14 sin 26o = x 12.6 ft. y 6.1 ft. x

  12. Using Trigonometry 29 C A a c B

  13. Try on your own: x x 17.6 tan32o = opp. adj. tan32o 11 = 11 = x x = x tan 32o 11 11 0.6249 tan32o y

  14. A 20-ft wire supporting a flagpole forms a 35o angle with the flagpole. To the nearest foot, how high is the flagpole? Using Trigonometry 20 x

  15. Tallest Mountain in the World? Mount Everest – 29, 029 feet

  16. Tallest Building in the World? • The Burj Khalifa, Dubai – 2717 feet

  17. The Tallest Waterfall in the World? • Angel, Salto – Venezuela - 3,212 feet

  18. Clinometer

  19. DEFINITIONS • Theangle of elevationof an object as seen by an observer is the angle between the horizontal and the line from the object to the observer's eye (the line of sight). • If the object is below the level of the observer, then the angle between the horizontal and the observer's line of sight is called the angle of depression.

  20. How tall is the Empire State Building? Exact Answer: 1,250 feet tall 76.5° 300 ft

  21. 20,326.3 feet Since Mount Everest is 29, 029 feet tall, how far was Mr. Sharma from the mountain, if his angle of elevation was 55°?

  22. 3,243.6 feet Mr. Sharma is looking up at the waterfall in Angel, Salto – Venezuela, which is 3,212 feet tall, and has an angle of elevation of 82°. He wants to know the distance that his line of sight makes to the top of the waterfall?

  23. Using Trigonometry R 41 S T 47

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