A person 1.6 m tall is 20 m away from a tower and observes the angle of elevation of the top of the tower to be 45°. What is the height of the tower?
- 21.6 m
- 20.0 m
- 20.6 m
- None of these
Explanation
We can use tan to find the height.
Given:
Person's height = 1.6 m
Distance from tower = 20 m
Angle of elevation = 45°
Let h = height of tower above the person's eye level.
In the right triangle:
tan(45°) = opposite / adjacent = h / 20
We know tan(45°) = 1
So:
1 = h / 20
h = 20 m
This is the height from eye level to top of tower.
Total height of tower = h + person's height
= 20 m + 1.6 m
= 21.6 m
Last verified on 05-08-2026
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