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Applications and Models

Solve problems using right triangles, find missing sides/angles, calculate heights, angles of elevation, and depressions.

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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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