Angles of Elevation and Depression - Interactive Activity

Definitions and Main Ideas

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

1. Elevation looks up from the horizontal; depression looks down from the horizontal. The direction of the line of sight decides which one you have.
2. 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.
3. Because of that equality, a depression problem can be solved inside the triangle using the equal elevation angle at the far end.
4. Once the right triangle is identified, the tangent ratio connects the height and the horizontal distance in most elevation and depression problems.
5. If the observer's eye (or instrument) is above the ground, remember to add that height at the end.

Elevation and Depression Explorer

What to do: Drag the object: up for an angle of elevation, down for an angle of depression. Drag the tower top to change the observer's height. Watch the two marked angles — the angle at the observer and the equal angle inside the triangle at the object.

Name the Angle

What to do: Each scene marks one angle with a gold wedge. Name the marked angle: angle of elevation or angle of depression. A first miss gives a hint and another try; a second miss names the correct angle and explains it.

Solve the Scene

What to do: Work each scene one step at a time. First choose the statement or equation the scene calls for, then solve. The diagram labels a part only after its step has been answered.

Your Turn

What to do: Answer each question. A first miss gives a hint and another try; a second miss shows the full explanation. Your score counts first-try answers only.