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10th ICSE
IMPORTANT
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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.

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Important Questions on Heights and Distances

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.
HARD
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.
HARD
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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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 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.
HARD
10th ICSE
IMPORTANT
Concise Mathematics>Chapter 22 - Heights and Distances>EXERCISE>Q 8
From the top of a cliff, 60 metres high, the angles of depression of the top and bottom of a tower are observed to be 30° and 60°. Find the height of the tower.
HARD
10th ICSE
IMPORTANT
Concise Mathematics>Chapter 22 - Heights and Distances>EXERCISE>Q 9
A man on a cliff observes a boat, at an angle of depression 30°, which is sailing towards the shore to the point immediately beneath him. Three minutes later, the angle of depression of the boat is found to be 60°. Assuming that the boat sails at a uniform speed, determine how much more time it will take to reach the shore ?
HARD
10th ICSE
IMPORTANT
Concise Mathematics>Chapter 22 - Heights and Distances>EXERCISE>Q 9
A man on a cliff observes a boat, at an angle of depression 30°, which is sailing towards the shore to the point immediately beneath him. Three minutes later, the angle of depression of the boat is found to be 60°. Assuming that the boat sails at a uniform speed, determine the speed of the boat in metre per second, if the height of the cliff is 500m.