Angle of Elevation
Angle measured upward from a horizontal line.
Learning Objectives
- identify elevation and depression angles;
- draw correct horizontal reference lines;
- use alternate angles in diagrams;
- solve scale-drawing problems;
- interpret real-life height and distance situations.
Introduction
This lesson develops Elevation and Depression from meaning and patterns before moving to calculations. Look for what the quantities, shapes or symbols represent, then connect that idea to the method.
Key Notes
Read the definitions and key facts below carefully. Each rule is most useful when you can explain why it fits the situation, not simply recall it.
Elevation and Depression
Angle of Depression
Angle measured downward from a horizontal line.
Because horizontal lines are parallel, an angle of depression equals the corresponding angle of elevation.
Worked Example
From the top of a tower, the angle of depression to a car is 32°. The angle of elevation from the car to the tower top is also 32°.
Try It: Elevation and Depression
🧠 Let’s Think Together
Before calculating, identify the information given, the result required and the mathematical relationship that connects them. Predict whether the answer should be larger, smaller or unchanged, then use that prediction to check the result.
Practice Questions
- Define angle of elevation.
- Define angle of depression.
- An angle of depression is 41°. Find the matching angle of elevation.
- Why are the two angles equal?
- State the first line you should draw when setting up such a diagram.
✅ Check Your Work
Show answers and working
- An angle measured upward from the horizontal.
- An angle measured downward from the horizontal.
- 41°.
- They are alternate angles between parallel horizontal lines.
- A horizontal reference line.
Common Mistakes
- Choosing a rule before identifying what the question describes.
- Skipping working or changing notation part-way through a solution.
- Accepting an answer without checking its size, sign or units.
Exam Focus
Show the mathematical relationship you are using, keep notation consistent and give a clear final answer. Use a quick estimate, diagram or inverse operation to check that the result is reasonable.
Summary
- Both angles are measured from horizontal lines.
- Elevation looks upward; depression looks downward.