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10th ICSE
IMPORTANT
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A vertical tower stands on horizontal plane and is surmounted by a vertical flagstaff of height h metre. At a point on the plane, the angle of elevation of the bottom of the flagstaff is α and that of the top of flagstaff is β. Prove that the height of the tower is htanαtanβ-tanα

Important Questions on Heights and Distances

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10th ICSE
IMPORTANT
Concise Mathematics>Chapter 22 - Heights and Distances>EXERCISE>Q 8
With reference to the given figure, a man stands on the ground at point A, which is on the same horizontal plane as B, the foot of the vertical pole BC. The height of the pole is 10m. The man's eye is 2m above the ground. He observes the angle of elevation of C, the top of the pole, as x° where tanx°=25. Calculate the distance AB in meters.
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10th ICSE
IMPORTANT
Concise Mathematics>Chapter 22 - Heights and Distances>EXERCISE>Q 8
With reference to the given figure, a man stands on the ground at point A, which is on the same horizontal plane as B, the foot of the vertical pole BC. The height of the pole is 10m. The man's eye is 2m above the ground. He observes the angle of elevation of C, the top of the pole, as x° where tanx°=25. Calculate angle of elevation of the top of the pole when he is standing 15 metres from the pole. Give your answer to the nearest degree.
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10th ICSE
IMPORTANT
Concise Mathematics>Chapter 22 - Heights and Distances>EXERCISE>Q 9
The angles of elevation of the top of a tower from two points on the ground at distances a and b meters from the base of the tower and in the same straight line with it are complementary. If the height of the tower is k meter, then k=
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10th ICSE
IMPORTANT
Concise Mathematics>Chapter 22 - Heights and Distances>EXERCISE>Q 10

From a window A, 10 m above the ground the angle of elevation of the top C of a tower is x°, where tanx°=52 and the angle of depression of the foot D of the tower is y°, where tany°=14·(see the given figure). Calculate the height CD of the tower in metres.

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10th ICSE
IMPORTANT
Concise Mathematics>Chapter 22 - Heights and Distances>EXERCISE>Q 11
A vertical tower is 20m high. A man standing at some distance from the tower knows that the cosine of the angle of elevation of the top of the tower is 0.53. How far is he standing from the foot of the tower?
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10th ICSE
IMPORTANT
Concise Mathematics>Chapter 22 - Heights and Distances>EXERCISE>Q 12
A man standing on the bank of a river observes that the angle of elevation of a tree on the opposite bank is 60°. When he moves 50 m away from the bank, he finds the angle of elevation to be 30°. Calculate the width of the river
HARD
10th ICSE
IMPORTANT
Concise Mathematics>Chapter 22 - Heights and Distances>EXERCISE>Q 12
A man standing on the bank of a river observes that the angle of elevation of a tree on the opposite bank is 60°. When he moves 50 m away from the bank, he finds the angle of elevation to be 30°. Calculate the height of the tree
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10th ICSE
IMPORTANT
Concise Mathematics>Chapter 22 - Heights and Distances>EXERCISE>Q 13
A 20m high vertical pole and a vertical tower are on the same level ground in such a way that the angle of elevation of the top of the tower, as seen from the foot of the pole, is 60° and the angle of elevation of the top of the pole as seen from the foot of the tower is 30°. Find the height of the tower.