Heights & distances
Find heights of towers and trees using angles of elevation.
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To find a tall height, draw a right triangle and use tan.
Look: Looking up at the top of a tower makes a right triangle.
✏️ Your turn!
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1Look up 45° from 20 m away. Height?
2A pole 6 m tall casts a 6 m shadow. Sun angle?
3tan 30° ≈ 0.58. 20 m away, look up 30°. Height?
! Careful!
✗Using sin with height and ground distance.
✓Opposite and adjacent → tan.
✗Measuring the angle from straight up.
✓Measure from flat (the ground).
See the whole lesson on one page
To find a tall height, draw a right triangle and use tan.
The height is opposite the angle. Your distance from the foot is adjacent. So tan(angle) = height ÷ distance.
Think of it like thisYou cannot climb a tall tree to measure it. But you can stand away from it and measure the angle you look up at.
- Angle of elevation
- How far you look up from flat.
Solved together
You stand 30 m from a tower. You look up 60° to see its top. How tall is it? (tan 60° ≈ 1.73)
Height is opposite, 30 m is adjacent: use tan.
tan 60° = height ÷ 30Multiply both sides by 30.
height = 30 × 1.73 ≈ 52
AnswerAbout 52 m tall.
Now practise it
Kanakku makes new questions on heights & distances every time. It shows the working and gives a hint when you are stuck.