Heights and Distances
ICSE · Class 10 · Mathematics
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A ladder of length 10 m leans against a wall and makes an angle of 60° with the ground. What is the height of the wall that the ladder touches?
From a point 20 m away from the base of a tower, the angle of elevation to the top is 30°. What is the height of the tower?
A man stands on top of a 50 m tall building and observes a car on the road with an angle of depression of 45°. How far is the car from the base of the building?
The angle of elevation of the top of a tree from a point 15 m away is 60°. Find the height of the tree.
Sample Questions
Which trigonometric ratios are commonly used in height and distance problems?
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sin θ, cos θ, tan θ
In height and distance problems, we primarily use sin θ (opposite/hypotenuse), cos θ (adjacent/hypotenuse), and tan θ (opposite/adjacent) as they directly relate to the sides we need to find.
A flagpole casts a shadow of 12 m when the sun's angle of elevation is 45°. What is the height of the flagpole?
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12 m
Using tan 45° = height/shadow. tan 45° = 1, so height = shadow × tan 45° = 12 × 1 = 12 m
From the top of a lighthouse 60 m high, the angle of depression of a boat is 30°. How far is the boat from the lighthouse?
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60√3 m
Using tan 30° = height/distance. tan 30° = 1/√3, so distance = 60/(1/√3) = 60√3 m ≈ 103.92 m
Which of the following statements about angles of elevation and depression are correct?
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Angle of elevation is measured upward from horizontal, Angle of depression is measured downward from horizontal
Angles of elevation and depression are always measured from the horizontal line, with elevation going up and depression going down. In practical problems, these are typically acute angles (less than 90°).
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