Angles of Elevation and Depression
The angle of elevation is measured upward from the horizontal, and the angle of depression is measured downward from it.
▶ Interact
Play with the controls to see the idea in action.
📘 Learn
The angle of elevation is measured upward from the horizontal, and the angle of depression is measured downward from it.
- Both are measured from the horizontal
- Elevation and depression are equal alternate angles
- Use tangent to find heights
🧠 Quick quiz
Three questions. Score 2 or more to complete the topic.
What is Angles of Elevation and Depression?
Within Mathematics, which covers numbers, algebra, geometry, trigonometry and statistics from first principles to exam level, this topic explains Angles of Elevation and Depression. Maths builds step by step, so each topic here gives you a rule, a picture and a quick check you can use on homework and in exams.
Check that you can explain Angles of Elevation and Depression in your own words and give one example from everyday life. If you can do that, you have understood the core idea.
Understanding Angles of Elevation and Depression gives you a reliable method you will reuse in later maths units, in science lessons and in data work.
Angles of Elevation and Depression in detail
The angle of elevation is the angle measured upward from the horizontal to a line of sight, such as looking up at the top of a tower. The angle of depression is the angle measured downward from the horizontal, such as looking down from a cliff at a boat.
The angle of elevation from point A to point B equals the angle of depression from B to A, because the horizontals are parallel and the angles are alternate. Drawing a clear right-angled triangle and applying sine, cosine or tangent solves problems about heights and distances.
How the interactive helps you understand Angles of Elevation and Depression
Watch the triangle in the interactive. Use any sliders or buttons it offers to change the values and see how the triangle responds.
Before you change anything, predict the result. Then change one value at a time and check whether your prediction was right. This is a quick way to build a correct mental model of Angles of Elevation and Depression.
Real-life uses and examples
- Use Angles of Elevation and Depression when comparing prices, discounts or recipe quantities in everyday life.
- Explain Angles of Elevation and Depression to a friend with a simple picture, such as a row of tiles or a bag of sweets.
- Spot Angles of Elevation and Depression in exam questions, where it often sits inside a short word problem.
Common mistakes to avoid
- Forgetting units, signs or brackets when you apply Angles of Elevation and Depression.
- Memorising the steps for Angles of Elevation and Depression without checking why they work.
- Learning the definition without testing it. Use the quiz and the interactive to check that you can apply the idea.
Frequently asked questions about Angles of Elevation and Depression
What is Angles of Elevation and Depression?
The angle of elevation is measured upward from the horizontal, and the angle of depression is measured downward from it.
What are the most important points about Angles of Elevation and Depression?
The main points are: Both are measured from the horizontal; Elevation and depression are equal alternate angles; Use tangent to find heights.
Why is Angles of Elevation and Depression useful?
Understanding Angles of Elevation and Depression gives you a reliable method you will reuse in later maths units, in science lessons and in data work.
How can I practise Angles of Elevation and Depression?
Open the interactive at the top of this page and change the controls one at a time. Predict the result before each change, then take the three-question quiz. A score of two or more marks the topic as complete on this device.
Which topics are related to Angles of Elevation and Depression?
Related topics in Mathematics include Pyramids, Cones and Spheres, Rotation and Enlargement, Probability Basics.