8.2.1 Angles of Elevation and Depression Key Objectives • Solve problems involving angles of elevation and angles of depression. Key Terms • An angle of elevation is the angle formed by a horizontal line and a line of sight to a point above the line. • An angle of depression is the angle formed by a horizontal line and a line of sight to a point below the line. Example 1 Classifying Angles of Elevation and Depression Angles are classified as angles of elevation or angles of depression in this example.
∠ 1 is an angle of depression because it is formed by a line of sight that is below a horizontal line. ∠ 2 is an angle of elevation because it is formed by a line of sight that is above a horizontal line. ∠ 3 is an angle of depression because it is formed by a line of sight that is below a horizontal line. ∠ 4 is an angle of elevation because it is formed by a line of sight that is above a horizontal line.
Example 2 Finding Distance by Using Angle of Elevation
A horizontal distance is calculated using an angle of elevation in this example. The angle of elevation is given. Also, the altitude of the object, or the length of the leg opposite the angle of elevation, is given. If x is the horizontal distance from the airport to the jet, then tan 37 ° = 6000/ x (the opposite leg over the adjacent leg). Solving for x yields a distance of approximately 7962 feet.
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