Q1. From a point 50 m from the base of a tower, the angle of elevation to the top is 30°. Find the height of the tower.
tanθ = height / distance
tan30° = h / 50 ⇒ h = 50 × tan30°
h = 50 × (1/√3) ≈ 28.9 m
Some Applications of Trigonometry — Class 10
Find the height of a tower without climbing it. Enter the distance and angle of elevation to get the height instantly.
Angle of elevationThe angle from the horizontal UP to an object (e.g. looking up at the top of a tower).
Angle of depressionThe angle from the horizontal DOWN to an object (e.g. looking down from a cliff). Equal to the angle of elevation from the other point.
Line of sightThe straight line from the observer's eye to the object being viewed.
Height & distance calculator Interactive
Enter the horizontal distance and the angle of elevation to find the height of the object.
Height, h = d·tanθ—m
This assumes the observer's eye is at ground level. If it is at height e, add e to the result.
Numericals practice Interactive
Height-and-distance problems with steps.
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Solved examples
Formula sheet
| Quantity | Formula |
|---|---|
| Height from angle of elevation | h = d × tanθ |
| Distance from height and angle | d = h / tanθ |
| Line of sight (hypotenuse) | l = d / cosθ |
Common mistakes & exam wins
- Always draw a right-triangle diagram first — it makes the ratio to use obvious.
- Angle of elevation (looking up) = angle of depression (looking down) between the same two points.
- tanθ = opposite/adjacent = height/distance is the ratio used in almost every heights-and-distances question.
Frequently asked questions
What is the angle of elevation?
The angle between the horizontal and the line of sight when looking UP at an object.
What is the angle of depression?
The angle between the horizontal and the line of sight when looking DOWN at an object, from a higher point.
What formula is used to find height in these problems?
h = d × tanθ, where d is the horizontal distance and θ the angle of elevation.