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GEOMETRY Solving Right Triangles

GEOMETRY Solving Right Triangles. Warm Up. Use your calculator to find each trigonometric ratio. Round to the nearest hundredth. 1) sin 63˚ 2) cos 27˚ 3) tan 64˚. Right Triangles. You can use trigonometric ratios to change a percent grade to an angle measure.

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GEOMETRY Solving Right Triangles

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  1. GEOMETRY Solving Right Triangles CONFIDENTIAL

  2. Warm Up Use your calculator to find each trigonometric ratio. Round to the nearest hundredth. 1) sin 63˚ 2) cos 27˚ 3) tan 64˚ CONFIDENTIAL

  3. Right Triangles You can use trigonometric ratios to change a percent grade to an angle measure. CONFIDENTIAL

  4. Angles from Trigonometric Ratios Use the trigonometric ratio cos A = 0.6 determine which angle of the triangle is /A. Cosine is the ratio of the adjacent leg to the hypotenuse. The leg adjacent to /1 is 3.6. The hypotenuse is 6. The leg adjacent to /2 is 4.8. The hypotenuse is 6. CONFIDENTIAL

  5. Now you try! Use the given trigonometric ratio to determine which angle of the triangle is /A. 1a) sin A = 8/17 1b) tan A = 1.875 CONFIDENTIAL

  6. Inverse Trigonometric Functions CONFIDENTIAL

  7. Calculating Angle Measures from Trigonometric Ratios Use your calculator to find each angle measure to the nearest degree. CONFIDENTIAL

  8. Now you try ! Use your calculator to find each angle measure to the nearest degree. CONFIDENTIAL

  9. Solving Right Triangles Find the unknown measures. Round lengths to the nearest hundredth and angle measures to the nearest degree. CONFIDENTIAL

  10. Now you try! Find the unknown measures. Round lengths to the nearest hundredth and angle measures to the nearest degree. CONFIDENTIAL

  11. Y Solving a Right Triangle in the Coordinate Plane The coordinates of the vertices of ∆JKL are J(-1,2), K(-1,-3), and L(3,-3). Find the side lengths to the nearest hundredth and the angle measures to the nearest degree. X Next page  CONFIDENTIAL

  12. CONFIDENTIAL

  13. Now you try! The coordinates of the vertices of ∆RST are R(-3,5), S(4,5), and T(4,-2). Find the side lengths to the nearest hundredth and the angle measures to the nearest degree. CONFIDENTIAL

  14. Travel Application San Francisco’s Lombard Street is known as one of “the crookedest streets in the world.” The road’s eight switchbacks were built in the 1920s to make the steep hill passable by cars. If the hill has a percent grade of 84%, what angle does the hill make with a horizontal line? Round to the nearest degree. 84 % = 84/100 Change the percent grade to a fraction An 84% grade means the hill rises 84 ft for every 100 ft of horizontal distance. Next page  CONFIDENTIAL

  15. Draw a right triangle to represent the hill. /A is the angle the hill makes with a horizontal line. CONFIDENTIAL

  16. Now you try! Baldwin St. in Dunedin, New Zealand, is the steepest street in the world. It has a grade of 38%. To the nearest degree, what angle does Baldwin St. make with a horizontal line? CONFIDENTIAL

  17. Now some practice problems for you! CONFIDENTIAL

  18. Assessment Use the given trigonometric ratio to determine which angle of the triangle is /A . CONFIDENTIAL

  19. Use your calculator to find each angle measure to the nearest degree. 4) 5) 6) CONFIDENTIAL

  20. Multi-Step Find the unknown measures. Round lengths to the nearest hundredth and angle measures to the nearest degree. 8) 7) CONFIDENTIAL

  21. 9) Find the side lengths to the nearest hundredth and the angle measures to the nearest degree for the given triangle. D(4,1), E(4,-2), F(-2,-2) 10) A hill in the Tour de France bike race has a grade of 8%. To the nearest degree, what is the angle that this hill makes with a horizontal line? CONFIDENTIAL

  22. Let’s review Angles from Trigonometric Ratios Use the trigonometric ratio cos A = 0.6 determine which angle of the triangle is /A. Cosine is the ratio of the adjacent leg to the hypotenuse. The leg adjacent to /1 is 3.6. The hypotenuse is 6. The leg adjacent to /2 is 4.8. The hypotenuse is 6. CONFIDENTIAL

  23. Inverse Trigonometric Functions CONFIDENTIAL

  24. Calculating Angle Measures from Trigonometric Ratios Use your calculator to find each angle measure to the nearest degree. CONFIDENTIAL

  25. Solving Right Triangles Find the unknown measures. Round lengths to the nearest hundredth and angle measures to the nearest degree. CONFIDENTIAL

  26. Travel Application San Francisco’s Lombard Street is known as one of “the crookedest streets in the world.” The road’s eight switchbacks were built in the 1920s to make the steep hill passable by cars. If the hill has a percent grade of 84%, what angle does the hill make with a horizontal line? Round to the nearest degree. 84 % = 84/100 Change the percent grade to a fraction An 84% grade means the hill rises 84 ft for every 100 ft of horizontal distance. Next page  CONFIDENTIAL

  27. Draw a right triangle to represent the hill. /A is the angle the hill makes with a horizontal line. CONFIDENTIAL

  28. Y Solving a Right Triangle in the Coordinate Plane The coordinates of the vertices of ∆JKL are J(-1,2), K(-1,-3), and L(3,-3). Find the side lengths to the nearest hundredth and the angle measures to the nearest degree. X Next page  CONFIDENTIAL

  29. Y X Next page  CONFIDENTIAL

  30. CONFIDENTIAL

  31. You did a great job today! CONFIDENTIAL

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