Trigonometry · SS 1
Angles of elevation and depression
Find the height of a tree, pole or building from how far away you are and the angle you look up.
- height = distance × tan θ
What the letters mean
- θ
- the angle of elevation (looking up from the horizontal)
- distance
- the horizontal distance to the object
Worked example
From 20 m away, the top of a mast is at an angle of elevation of 60°. How tall is the mast?
Step 1: Opposite = height, adjacent = 20 m
height = 20 × tan 60°
Step 2: tan 60° ≈ 1.732
height = 20 × 1.732 ≈ 34.6 m
Final answer: about 34.6 m
The angle of depression from the top equals the angle of elevation from the bottom (alternate angles).
See it
Play with this picture from the Angles of Elevation and Depression lesson.
height = 40 × tan 35° = 40 × 0.7002 = 28.01 m
Elevation (looking up) = depression (looking down): alternate angles between the two horizontal lines.
Angle θ35°
Distance40 m