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Mathematics at Work 11
Geometry
4. Solve problems involving scale
4.6 Angle of elevation and depression
Angle of Elevation and Depression
The angle of elevation is measured up from the horizontal; the angle of depression is measured down.
What You'll Learn
The angle of elevation is measured up from the horizontal; the angle of depression is measured down.
Both angles are measured from the horizontal, never from the vertical.
The angle of depression equals the angle of elevation (alternate interior angles).
Solve the right triangle with the tangent, sine, or cosine ratio.
Example: at 40 m with a 35 degree elevation, the height is 40 times tan 35, about 28 m.
What You'll Practice
1
Finding heights of objects using angle of elevation and known distances
2
Calculating distances using angle of depression and known heights
3
Solving problems with shadows and light sources
4
Working with two-building scenarios involving both angles
5
Breaking complex problems into multiple right triangles
Why This Matters
Angles of elevation and depression are essential for real-world applications like surveying land, estimating building heights, navigation, and aviation. You'll use these skills in engineering, architecture, physics, and any field requiring distance or height measurements that can't be obtained directly.
This Unit Includes
6 Video lessons
Practice exercises
Learning resources
Skills
Angle of Elevation
Angle of Depression
Trigonometry
Right Triangles
Tangent Ratio
Word Problems
Real-World Applications
NS Curriculum Aligned