Angles of Elevation and Depression
Angles measured up or down from the horizontal.
About this topic
An angle of elevation is measured upward from the horizontal to a line of sight, such as looking up at a kite. An angle of depression is measured downward from the horizontal, like looking down from a cliff at a boat. Because horizontal lines are parallel, the two angles are equal as alternate interior angles.
Both angles are always measured from a horizontal reference line, never from the vertical. Drawing a clear diagram turns the story into a right triangle, where the height is the opposite side, the ground distance is the adjacent side and the line of sight is the hypotenuse. Then tan, sin or cos does the rest.
Example: standing 50 m from a tall building, you measure an angle of elevation of 40° to the top. The height above your eye level is 50 × tan 40°, about 42 m; add your eye height to get the building height. If a lighthouse keeper 30 m up sees a boat at a 5° depression, the boat is 30 / tan 5°, roughly 343 m away.
These angles are used in surveying, aviation, navigation and search and rescue. A frequent mistake is placing the depression angle inside the triangle at the wrong vertex; remember that it equals the elevation angle from the boat looking back up, which is the angle inside the triangle at the boat.
Key ideas
- Elevation looks up
- Depression looks down
- They are equal alternate angles
Quick check
Use cases: where Angles of Elevation and Depression helps
- Homework: review the key idea behind Angles of Elevation and Depression before you start a problem set.
- Exam revision: use the quick check to test whether you can recall Angles of Elevation and Depression without notes.
- Visual learning: play with the interactive lab to see how Angles of Elevation and Depression changes when you adjust its inputs.
- Teaching a friend: explain Angles of Elevation and Depression in your own words, then compare your version with the key ideas.
Number and algebra skills are used in science, engineering, budgeting and computing.
Frequently asked questions
What is Angles of Elevation and Depression?
Angles measured up or down from the horizontal.
What will I learn in Angles of Elevation and Depression?
Elevation looks up. Depression looks down. They are equal alternate angles.
Is Angles of Elevation and Depression part of Mathematics?
Yes. It is one of 200 Mathematics topics on LearnViz HighSchoolEdu, with 3 key ideas, a live animation and a quick check.
Does the Angles of Elevation and Depression lab work on a phone or tablet?
Yes. The animation resizes to fit your screen and supports touch, so you can drag, tap and slide with your finger.
How should I study Angles of Elevation and Depression?
Read the summary and key ideas first, play with the interactive lab to see the idea in motion, then answer the quick check. If you get a question wrong, go back to the key idea it tests.
Do I need an account, and is my progress saved?
No account is needed. Marking a topic as learned is saved in your own browser, so it stays on that device and is not sent to a server.