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Applications and Models

Applications and Models. Objective: To solve a variety of problems using a right triangle. Example 1. Solve the right triangle for all missing sides and angles. Example 1. Solve the right triangle for all missing sides and angles. The angles of the triangle

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Applications and Models

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  1. Applications and Models Objective: To solve a variety of problems using a right triangle.

  2. Example 1 • Solve the right triangle for all missing sides and angles.

  3. Example 1 • Solve the right triangle for all missing sides and angles. • The angles of the triangle need to add to 1800. 1800 – 900 – 34.20 = 55.80

  4. Example 1 • Solve the right triangle for all missing sides and angles.

  5. Example 1 • Solve the right triangle for all missing sides and angles.

  6. You Try • Solve the right triangle for all missing sides and angles.

  7. You Try • Solve the right triangle for all missing sides and angles. • The missing angle is

  8. You Try • Solve the right triangle for all missing sides and angles.

  9. You Try • Solve the right triangle for all missing sides and angles.

  10. Example 2 • A safety regulation states that the maximum angle of elevation for a rescue ladder is 720. A fire department’s longest ladder is 110 feet. What is the maximum safe rescue height?

  11. Example 2 • A safety regulation states that the maximum angle of elevation for a rescue ladder is 720. A fire department’s longest ladder is 110 feet. What is the maximum safe rescue height? • We need to solve for a.

  12. Example 3 • At a point 200 feet from the base of a building, the angle of elevation to the bottom of a smokestack is 350, whereas the angle of elevation to the top is 530. Find the height s of the smokestack alone.

  13. Example 3 • At a point 200 feet from the base of a building, the angle of elevation to the bottom of a smokestack is 350, whereas the angle of elevation to the top is 530. Find the height s of the smokestack alone. • First, we find the height to the top of the smokestack.

  14. Example 3 • At a point 200 feet from the base of a building, the angle of elevation to the bottom of a smokestack is 350, whereas the angle of elevation to the top is 530. Find the height s of the smokestack alone. • Next, we find the height of the building.

  15. Example 3 • At a point 200 feet from the base of a building, the angle of elevation to the bottom of a smokestack is 350, whereas the angle of elevation to the top is 530. Find the height s of the smokestack alone. • We subtract the two values to find the height of the smokestack.

  16. Example 4 • A swimming pool is 20 meters long and 12 meters wide. The bottom of the pool is slanted so that the water depth is 1.3 meters at the shallow end and 4 meters at the deep end, as shown. Find the angle of depression of the bottom of the pool.

  17. Example 4 • A swimming pool is 20 meters long and 12 meters wide. The bottom of the pool is slanted so that the water depth is 1.3 meters at the shallow end and 4 meters at the deep end, as shown. Find the angle of depression of the bottom of the pool.

  18. Trig and Bearings • In surveying and navigation, directions are generally given in terms of bearings. A bearing measures the acute angle that a path or line of sight makes with a fixed north-south line. Look at the following examples.

  19. Trig and Bearings • In surveying and navigation, directions are generally given in terms of bearings. A bearing measures the acute angle that a path or line of sight makes with a fixed north-south line. Look at the following examples.

  20. Trig and Bearings • You try. Draw a bearing of: W200N E300S

  21. Trig and Bearings • You try. Draw a bearing of: W200N E300S

  22. Class work • Pages 521-522 • 2-8 even

  23. Homework • Pages 521-522 • 1-7 odd • 15-21 odd • 27, 29, 31

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