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Understanding Angles of Elevation and Depression in Real-Life Applications

This chapter explores the concepts of angles of elevation and depression, supported by real-world examples. An angle of elevation is formed between the horizontal line and the line of sight to a point above the horizontal, while an angle of depression is formed for a point below. Through practical scenarios such as measuring the height of cliffs, buildings, and airplanes' descent angles, students will learn how to apply trigonometric principles. Engage with examples to find distances and heights using angles, preparing for your upcoming test on right triangle trigonometry.

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Understanding Angles of Elevation and Depression in Real-Life Applications

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  1. Chapter 9 9-3 Angles of Elevation and Depression

  2. Angle of Elevation • The angle formed by the horizontal and the line of sight to a point above horizontal

  3. Angle of Depression • The angle formed by the horizontal and the line of sight to a point below horizontal

  4. Example #1 • Describe 1 and 2.

  5. Example #2 • You sight a rock climber on a cliff at a 32° angle of elevation. The horizontal ground distance to the cliff is 1000 ft. Find the line of sight distance to the rock climber.

  6. Example #3 • A surveyor stands 200 ft from a building to measure its height with a 5 ft tall theodolite. The angle of elevation to the top of the building is 35°. How tall is the building?

  7. Example #4 • Find the height of the arch.

  8. Example #5 • To approach the airport, the pilot must begin a 3° descent starting from an altitude of 2714 ft. The airport altitude is 1007 ft. How many miles from the runway is the airplane at the start of this approach?

  9. Example #6 • An airplane pilot sights a life raft at a 26° angle of depression. The airplane’s altitude is 3 km. What is the airplane’s surface distance d from the raft?

  10. Example #7 • An airplane flying 3500 ft above ground begins a 2° descent to land at an airport. How many miles from the airport is the airplane when it starts its descent?

  11. Example #8 • Two buildings are 30 ft apart. The angle of elevation from the top of one to the top of the other is 19°. What is their difference in height?

  12. My Homework is… Review—next class (Wednesday) Right Triangle Trig Test—Friday!

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