Obj. 42 Angles of Elevation and Depression
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This document discusses angles of elevation and depression. It defines an angle of elevation as formed between a horizontal line and the line of sight to a point above the line, while an angle of depression is formed between a horizontal line and the line of sight to a point below the line. It provides examples of how to identify if an angle is elevation or depression and how to solve problems involving these angles using trigonometric functions like tangent.
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Obj. 42 Angles of Elevation and Depression
- 1. Obj. 42 Elevation and Depression The student is able to (I can): • Solve problems involving angles of depression or elevation
- 2. angle of elevation This is an angle formed by a horizontal line and the line of sight to a point above the line. angle On the SAT, this is called the angle of inclination.
- 3. angle of depression This is an angle formed by a horizontal line and a line of sight to a point below the line. angle On the SAT, this is called the angle of declination.
- 4. These two angles are related because the horizontal lines are parallel: To identify whether an angle is an angle of elevation or depression, check whether the line of sight is above or below the horizontal line.
- 5. Identify whether the angle is an angle of elevation or depression. 1. ∠1 depression 2. ∠2 elevation 3. ∠3 depression 4. ∠4 elevation
- 6. Examples 1. If a tree casts a shadow 18 feet long when the sun is at an elevation of 35˚, how tall is the tree to the nearest foot? x (opp) 35˚ 18‘ (adj) x tan35° = 18 x = 18 tan35° x = 13 feet
- 7. 2. A plane, at an altitude of 3000 feet, observes the airport at an angle of 27˚. What is the horizontal distance between the plane and the airport to the nearest foot? 27˚ 3000’ (opp) (27˚) x (adj) 3000 tan27° = x 3000 x= tan27° x = 5888 feet