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10th ICSE
IMPORTANT
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In the figure, given below, it is given that AB is perpendicular to BD and is of length X metres. DC=30m,∠ADB=30° and ∠ACB=45°

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Important Questions on Heights and Distances

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10th ICSE
IMPORTANT
Concise Mathematics>Chapter 22 - Heights and Distances>EXERCISE>Q 2
Find the height of a tree when it is found that on walking away from it 20m, in a horizontal line through its base, the elevation of its top changes from 60° to 30°.
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10th ICSE
IMPORTANT
Concise Mathematics>Chapter 22 - Heights and Distances>EXERCISE>Q 3
Find the height of a building, when it is found that on walking towards it 40m in a horizontal line through its base the angular elevation of its top changes from 30° to 45°.
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10th ICSE
IMPORTANT
Concise Mathematics>Chapter 22 - Heights and Distances>EXERCISE>Q 4
From the top of a lighthouse 100m high, the angles of depression of two ships are observed as 48° and 36° respectively. Find the distance between the two ships (in the nearest meter) if the ships are on the same side of the lighthouse.
HARD
10th ICSE
IMPORTANT
Concise Mathematics>Chapter 22 - Heights and Distances>EXERCISE>Q 4
From the top of a lighthouse 100m high, the angles of depression of two ships are observed as 48° and 36° respectively. Find the distance between the two ships (in the nearest metre) if the ships are on the opposite sides of the lighthouse.
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10th ICSE
IMPORTANT
Concise Mathematics>Chapter 22 - Heights and Distances>EXERCISE>Q 5
Two pillars of equal heights stand on either side of a roadway, which is 150 m Wide. At a point in the roadway between the pillars the elevations of the tops of the pillars are 60° and 30°; find the height of the pillars and the position of the point.
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10th ICSE
IMPORTANT
Concise Mathematics>Chapter 22 - Heights and Distances>EXERCISE>Q 6

From the figure, given below, calculate the length of CD.

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10th ICSE
IMPORTANT
Concise Mathematics>Chapter 22 - Heights and Distances>EXERCISE>Q 7
The angle of elevation of the top of a tower is observed to be 60°. At a point, 30m vertically above the first point of observation, the elevation is found to be 45°. Find the height of the tower.
HARD
10th ICSE
IMPORTANT
Concise Mathematics>Chapter 22 - Heights and Distances>EXERCISE>Q 7
The angle of elevation of the top of a tower is observed to be 60°. At a point, 30m Vertically above the first point of observation, the elevation is found to be 45°. Find its horizontal distance from the points of observation.