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9.1 – Trigonometric Ratios (PART 1)

9.1 – Trigonometric Ratios (PART 1). Why is Trigonometry important ?. Flight of Planes Sound Waves (study in music theory classes) Current of the Ocean Architecture Navigation/Surveying Without Trig. we would have NEVER made it to the moon! Launch and Orbital Trajectories.

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9.1 – Trigonometric Ratios (PART 1)

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  1. 9.1 – Trigonometric Ratios (PART 1)

  2. Why is Trigonometry important? • Flight of Planes • Sound Waves (study in music theory classes) • Current of the Ocean • Architecture • Navigation/Surveying • Without Trig. we would have NEVER made it to the moon! • Launch and Orbital Trajectories

  3. Topic OneSolving for missing pieces of information.

  4. Right Triangle Trig. Functions • Let  be an acute angle of a right triangle. SOH CAH TOA

  5. A A Identifying the correct angle makes a difference!

  6. 15 Evaluate the Trig. Functions for hypotenuse 17 8 adjacent opposite

  7. 14 Evaluate the Trig. Functions for hypotenuse 23 opposite adjacent

  8. 47 15 x Find the Value of x THIS IS WHEN THE MODE OF YOU CALCULATOR MATTERS!!!! When you evaluate trig. functions at angles you need to be in the correct angle units. hypotenuse opposite

  9. x 31 15 Find the Value of x hypotenuse adjacent

  10. Topic TwoSolving for ALL of the missing pieces of information.

  11. Solving Right Triangles • When asked to SOLVE A RIGHT TRIANGLE • Find ALL missing sides • Find ALL missing angles • What to Use when solving a right triangle: • SOH – CAH – TOA • Pythagorean Thm. • Triangle Sum Thm. • Inverse Trig (solve for unknown angles)

  12. Pythagorean Thm. Triangle Sum Theorem All angles in a triangle add = 180∘

  13. 15 Inverse Trig – to find UNKNOWNangles!!! 18 Change your calc to radian mode and see what happens…

  14. Solve the Right Triangle 55∘ 10.65 Side c: OR Side a:

  15. Solve the Right Triangle Find side e: (Pythagorean triple!) e

  16. Topic ThreeAngles of Elevation and Depression

  17. Angle of Elevation & Depression

  18. Angle of Elevation • An ant looks up at the top of a tree with an angle of elevation of . (The ants height is negligible). If the tree is 15 feet tall, how far away is the ant from the top of the tree?

  19. Angle of Depression From the top of a vertical cliff 40 m high, the angle of depression of an object that is level with the base of the cliff is 34º. How far is the object from the base of the cliff?

  20. Homework • Topic One: Textbook Pg. 333#5, 6 • Topic Two: Textbook Pg. 334 #1, 2, 8 • Topic Three: Workbook Pg. 67 #16-18

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