Height and Distance Questions and Answers, Solutions, Multiple Choice Quiz – Recruitment, Syllabus, Result, Admit Card


Those candidates, who are searching for Height and Distance Questions and Answers, are at right place. From this page you can get Height and Distance Questions with Solutions by which you can easily crack your exam.

You must use trigonometric ratios which are tabulated below to determine heights and distances of different objects. Candidates can also prepare for exam through the Height and Distance Multiple Choice Quiz.

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Height and Distance Questions

Trigonometric Ratios of Standard Angles

∠C 0∘ 30∘ 45∘ 60∘ 90∘
sin C 12 1√2 √32 1
cos c 1 √32 1√2 12
tan C 1√3 1 √3 Not Defined
csc C Not Defined 2 √2 2√3 1
sec C 1 2√3 √2 2 Not Defined
cot C Not Defined √3 1 1√3

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Height and Distance Questions and Answers

Candidates are advised to solve out Height and Distance Questions which is given on this single page.

Question 1: Two ships are sailing in the sea on the two sides of a lighthouse. The angle of elevation of the top of the lighthouse is observed from the ships are 30° and 45° respectively. If the lighthouse is 100 m high, the distance between the two ships is:

  1. 173 m
  2. 200 m
  3. 273 m
  4. 300 m

Answer: 3

Question 2: A man standing at a point P is watching the top of a tower, which makes an angle of elevation of 30º with the man’s eye. The man walks some distance towards the tower to watch its top and the angle of the elevation becomes 60º. What is the distance between the base of the tower and the point P?

  1. 43 units
  2. 8 units
  3. 12 units
  4. Data inadequate
  5. None of these
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Answer: 4

Question 3: The angle of elevation of a ladder leaning against a wall is 60º and the foot of the ladder is 4.6 m away from the wall. The length of the ladder is:

  1. 3 m
  2. 6 m
  3. 8 m
  4. 2 m

Answer: 4

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Question 4: An observer 1.6 m tall is 203 away from a tower. The angle of elevation from his eye to the top of the tower is 30º. The heights of the tower is:

  1. 6 m
  2. 2 m
  3. 72 m
  4. None of these

Answer: 1

Question 5: From a point P on a level ground, the angle of elevation of the top tower is 30º. If the tower is 100 m high, the distance of point P from the foot of the tower is:

  1. 149 m
  2. 156 m
  3. 173 m
  4. 200 m

Answer: 3

Question 6: The angle of elevation of the sun, when the length of the shadow of a tree 3 times the height of the tree, is:

  1. 30º
  2. 45º
  3. 60º
  4. 90º

Answer: 1

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Question 7: When the sun’s altitude changes from 30° to 60°, the length of the shadow of a tower decreases by 70m. What is the height of the tower?

  1. 35 m
  2. 140 m
  3. 6 m
  4. 2 m
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Answer: 3

Question 8: A balloon leaves the earth at a point A and rises vertically at uniform speed. At the end of 2 minutes, John finds the angular elevation of the balloon as 60°. If the point at which John is standing is 150 m away from point A, what is the speed of the balloon?

  1. 63 meter/sec
  2. 16 meter/sec
  3. 87 meter/sec
  4. 72 meter/sec

Answer: 2

Question 9: From a tower of 80 m high, the angle of depression of a bus is 30°. How far is the bus from the tower?

  1. 40 m
  2. 4 m
  3. 24 m
  4. 160 m

Answer: 2

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Question 10: A man on the top of a vertical observation tower observes a car moving at a uniform speed coming directly towards it. If it takes 8 minutes for the angle of depression to change from 30° to 45°, how soon after this will the car reach the observation tower?

  1. 8 min 17 second
  2. 10 min 57 second
  3. 14 min 34 second
  4. 12 min 23 second

Answer: 2

Question 11: The angle of elevation of the sun, when the length of the shadow of a tree 3 times the height of the tree, is:

  1. 30º
  2. 45º
  3. 60º
  4. 90º

Answer: 1

Question 12 An aeroplane when 900 m high passes vertically above another aeroplane at an instant when their angles of elevation at same observing point are 60° and 45° respectively. Approximately, how many meters higher is the one than the other?

  1. 381 m
  2. 169 m
  3. 254 m
  4. 211 m
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Answer: 1

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Question 13: The top of a 15 metre high tower makes an angle of elevation of 60° with the bottom of an electronic pole and angle of elevation of 30° with the top of the pole. What is the height of the electric pole?

  1. 5 metres
  2. 8 metres
  3. 10 metres
  4. 12 metres

Answer: 3

Question 14: The angle of elevation of the top of a tower from a certain point is 30°. If the observer moves 40 m towards the tower, the angle of elevation of the top of the tower increases by 15°. The height of the tower is:

  1. 2 m
  2. 2 m
  3. 2 m
  4. 6 m

Answer: 4

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Question 15: A ladder 10 m long just reaches the top of a wall and makes an angle of 60° with the wall. Find the distance of the foot of the ladder from the wall (√3=1.73)

  1. 32
  2. 3 m
  3. 5 m
  4. 65 m

Answer: 1

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