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Heights and Distance Questions and Answers

Heights and Distance Questions

Formula

Definition of Heights and Distance

Heights and Distance is an important topic for examination point of view. The topic comprises questions where height of a building, angle of elevation, and depression are given for another building, which is close by. The question is to find the height of the second building. Most of these questions are found in trigonometry.

Terms

The angle of Elevation

It can be better understood by considering a situation where a person is standing on the ground and looking at an object which is present at some height, for instance, at the top of a building. In this case, the line that joins the eye of the man with the top of the building is known as the line of sight. The angle which is between the line of sight with the horizontal line is known as the angle of elevation.

The angle of Depression

In another situation where a person is standing at some height with respect to an object he is seeing. Here, also the line joining the eye of the man with the building’s bottom is called the line of sight. The angle made by the line of sight with the horizontal line is known as the angle of depression.

Question 1

Time: 00:00:00
A man is standing in his balcony, which is on the third floor of the building and is at the height of 10m. His angle of elevation at the top of the opposite building is 600, and the angle of depression of the base is 300. Determine the height of the building opposite to him?

40 mtrs

40 mtrs

50 mtrs

50 mtrs

70 mtrs

70 mtrs

100 mtrs

100 mtrs

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Question 2

Time: 00:00:00
A boy is standing on a riverbank. His angle of elevation from the treetop, which is on the opposite bank is 450. When he walks 20 meters away from his place, his angle of elevation becomes 300. What is the height of the tree?

7 m

7 m

5(√3 + 2)m

5(√3 + 2)m

10(√3 + 1)m

10(√3 + 1)m

None of the above

None of the above

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Question 3

Time: 00:00:00
Raj is standing on the top of a building which is 60 meters high. The angle of elevation and depression to the top and the foot of another building are α and β. What is the height of the second building?

cot β tan α

cot β tan α

60 (1 + cot β tan α)

60 (1 + cot β tan α)

60 (1 + tan α)

60 (1 + tan α)

None of the above

None of the above

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Question 4

Time: 00:00:00
From the top of a building, which is 75m high, the angles of depression of the top and the bottom of a pole which is present on the same plane as the building are 300 and 450, What is the pole’s height?

75m

75m

28.3m

28.3m

32m

32m

31.7m

31.7m

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Question 5

Time: 00:00:00
A tower is 50m high. The elevation angle to the top of the tower from the point on A on the ground is 300. Calculate the distance from the bottom of the tower and point A.

50√3

50√3

20√3

20√3

26

26

50√4

50√4

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Question 6

Time: 00:00:00
A girl is standing on the ground at a point P. If she looks at the topmost point of the building, the angle of elevation is 600. If the point P is 32 m from the building, what is its height?

30√5

30√5

20√2

20√2

32√3

32√3

90√2

90√2

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Question 7

Time: 00:00:00
A lighthouse is 80m high, a person observes two ships. The angles of elevation of both these ships as observed from the lighthouse are 450 and 300, What is the distance between the two ships?

40.36m

40.36m

58.56m

58.56m

89.36m

89.36m

None of the above

None of the above

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Question 8

Time: 00:00:00
A building which is 20 meters high, a man is flying a kite. He is using a thread that is 75m long to keep the kite in the air. If the thread is making an angle of 450 with the horizontal, then calculate the height of the kite from the ground.

70.36m

70.36m

78.3m

78.3m

56.3m

56.3m

63.3m

63.3m

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Question 9

Time: 00:00:00
A ground has two poles of height 30mtrs and 10mtrs on the ground. A wire connects both these poles of length 40mtrs. What is the angle made by the wire with the horizontal?

80 degree

80 degree

30 degree

30 degree

45 degree

45 degree

90 degree

90 degree

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Question 10

Time: 00:00:00
The angles of depression of the top and bottom of a tree, as observed from the top of a building, which is 90mtrs high are 300 and 600. What is the height of the tree?

60m

60m

20m

20m

10m

10m

50m

50m

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Question 11

Time: 00:00:00
The upper part of a pole is broken. The top of the pole touches the ground making an angle of 300. The distance of the point where the top touches the ground to the base of the pole is 72m. What is the height of the pole?

153.6m

153.6m

124.7m

124.7m

100m

100m

None of the above

None of the above