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Height and Distance Maths - Height and Distance

Maharashtra Board - STD 10 - Maths (MSBSHSE - Semi English Medium). 38 questions in this chapter.

Question types

Height and Distance question types

38 questions across 3 question groups — pick any mix to generate a Maths paper with step-by-step answer keys.

38
Questions
3
Question groups
5
Question types
Sample Questions

Height and Distance questions

One sample from each question group in this chapter. Select any group above to see the full set with answer keys.

Q 13 Marks Question3 Marks
The angle of depression from the top of a tower of a point A on the ground is 30°. On moving a distance of 20 metres from the point A towards the foot of the tower to a point B, the angle of elevation of the top of the tower from the point B is 60°. Find the height of the tower and its distance from the point A.
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Q 23 Marks Question3 Marks
From the top of a tower 100m high, a man observes two cars on the opposite sides of the tower and in same straight line with its base, with angles of depression 30° and 45° respectively. Find the distance between the cars. $\big[\text{Take}\sqrt{3}=1.732\big]$
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Q 33 Marks Question3 Marks
The angles of elevation of the top of a tower from two points at distances of 4m and 9m from the base of the tower and in the same straight line with it are complementary. Show that the height of the tower is 6 metres.
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Q 44 Marks Questions4 Marks
A statue 1.46m tall, stands on the top of pedestal. From a point on the ground, the angle of elevation of the top of the statue is 60° and from the same point, the angle of elevation of the top of the pedestal is 45°. Find the height of the pedestal. $\big[\text{Use}\sqrt{3}=1.732\big]$
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Q 54 Marks Questions4 Marks
A vertical tower stands on a horizontal plane and is surmounted by a vertical flagstaff of height 6m. At a point on the plane, the angle of elevation of the bottom of the flagstaff is 30° and that of the top of the flagstaff is 60°. Find the height of the tower. $\big[\text{Use}\sqrt{3}=1.732\big]$
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Q 64 Marks Questions4 Marks
From a point on the ground 40m away from the foot of a tower, the angle ofclevation of the top of the t wer is 30°. The angle of elevation of the top of a water tank (on the top of the tower) is 45°. Find:
  1. The height of the tower.
  2. The depth of the tank.
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Q 74 Marks Questions4 Marks
A tower stands vertically an the ground.From a point on the ground which is 20m away from the foot f the tower, th angle of elevation of its top is found tobe 60°. Find theh ight of the tower. $\big[\text{Take}\sqrt{3}=1.732\big]$
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Q 84 Marks Questions4 Marks
An electrician has to repair an electric fault on a pole of height 4 metres. He needs to reach a point 1 metre below the top of the pole to undertake the repair work. What should be the length of the ladder that he should use, which when inclined at an angle of 60° to the horizontal would enable him to reach the required position? $\big[\text{Use}\sqrt{3}=1.73\big]$
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Q 95 Marks Question5 Marks
As observed from the top of a lighthouse, 100m above sea level, the angle of depression of a ship, sailing directly towards it, changes from 30° to 60°. Determine the distance travelled by the ship during the period of observation. $\big[\text{Use}\sqrt{3}=1.732\big]$
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Q 105 Marks Question5 Marks
The angle of elevation of the top Q of a vertical tower PQ from a point X on the ground is 60°. At a point Y, 40m vertically above X, the angle of elevation is 45°. Find the height of tower. $\big[\text{Take}\sqrt{3}=1.732\big]$
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Q 115 Marks Question5 Marks
An aeroplane is flying at a height of 300m above the ground. Flying at this height the angles of depression on from the two aeoplane of two points on both banks of a river in opposite directions are 45° and 60° respectively. Find the width of the river. $\big[\text{Use}\sqrt{3}=1.732\big]$
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Q 125 Marks Question5 Marks
From the top of a building AB, 60m high, the an es of depression of the top and bottom of a vertical lamp-post CD are obseved to be 30° and 60° respetively. Find:
  1. The horizontal distance between AB and CD,
  2. The height of the lamp post,
  3. The difference between the heights of the building and the lamp-post.
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Q 135 Marks Question5 Marks
From a point on a bridge across a river, the angles of depression of the banks on opposite sides of the river are 30° and 45° resbectively. If the bridge is at a height of 2.5m from the banks, find the width of the river.$\big[\text{Take}\sqrt{3}=1.732\big]$
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