Angles of Elevation and Depression
Overview
Angles of elevation and depression describe looking up or looking down along a line of sight, measured from the horizontal. This lesson identifies each angle in a diagram — remembering that the angle of depression sits outside the triangle while the angle of elevation sits inside it — uses the fact that the two angles are equal (alternate interior angles formed by parallel horizontal lines), and applies the trigonometric ratios to find heights and distances in real situations.
Vocabulary
- Line of Sight
- The line from an observer's eye to the object being viewed.
- Angle of Elevation
- The angle formed by the horizontal line through the observer and the line of sight to an object above the observer. It is measured from the ground up and is always inside the triangle.
- Angle of Depression
- The angle formed by the horizontal line through the observer and the line of sight to an object below the observer. It is measured down from the horizon line and is always outside the triangle.
- Horizontal Line
- The reference line through the observer, parallel to the ground, from which angles of elevation and depression are measured.
Main Ideas
- Elevation looks up from the horizontal; depression looks down from the horizontal. The direction of the line of sight decides which one you have.
- The horizon line is parallel to the ground, so the angle of depression from an observer equals the angle of elevation from the object being viewed — they are alternate interior angles.
- Because of that equality, a depression problem can be solved inside the triangle using the equal elevation angle at the far end.
- Once the right triangle is identified, the tangent ratio connects the height and the horizontal distance in most elevation and depression problems.
- If the observer's eye (or instrument) is above the ground, remember to add that height at the end.
Lesson Notes
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Practice Problems
Want More Practice?
Download the practice worksheet for this lesson, work the problems, then check your work with the solutions.