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Height and Distance problems


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

  • Options
  • A. 4√3 units
  • B. 8 units
  • C. 12 units
  • D. Data inadequate
  • E. None of these
  • Discuss
  • 2. The angle of elevation of a ladder leaning against a wall is 60° and the foot of the ladder is 4.6 m away from the wall. The length of the ladder is:

  • Options
  • A. 2.3 m
  • B. 4.6 m
  • C. 7.8 m
  • D. 9.2 m
  • Discuss
  • 3. An observer 1.6 m tall is 20√3 away from a tower. The angle of elevation from his eye to the top of the tower is 30°. The heights of the tower is:

  • Options
  • A. 21.6 m
  • B. 23.2 m
  • C. 24.72 m
  • D. None of these
  • Also asked in: AIEEE, Bank Exams, CAT, Analyst, Bank Clerk, Bank PO

  • Discuss
  • 4. From a point P on a level ground, the angle of elevation of the top tower is 30°. If the tower is 100 m high, the distance of point P from the foot of the tower is:

  • Options
  • A. 149 m
  • B. 156 m
  • C. 173 m
  • D. 200 m
  • Discuss
  • 5. The angle of elevation of the sun, when the length of the shadow of a tree √3 times the height of the tree, is:

  • Options
  • A. 30°
  • B. 45°
  • C. 60°
  • D. 90°
  • Discuss
  • 6. 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:

  • Options
  • A. 173 m
  • B. 200 m
  • C. 273 m
  • D. 300 m
  • Discuss
  • 7. 
    The angle of elevation of a ladder leaning against a wall is 60º and the foot of the ladder is 12.4 m away from the wall. The length of the ladder is :

  • Options
  • A. 14.8 m
  • B. 24.8 m
  • C. 6.2 m
  • D. 12.4 m
  • Discuss
  • 8. 
    A person standing on the bank of a river observes that the angle subtended by a tree on the opposite bank is 60°, when he retires 40 meters from the bank then he find the angle to be 30°. Then the breadth of the river is?

  • Options
  • A. 40 m
  • B. 60 m
  • C. 20 m
  • D. 30 m
  • Discuss
  • 9. 
    A man is observing from the top of a tower a boat speeding away from the tower. The boat makes an angle of depression of 45° with the man's eye when at a distance of 60 m from the tower. After 5 second, the angle of depression becomes 30°, Find the speed of the boat, assuming that it is running in still water.

  • Options
  • A. 30 km/hr.
  • B. 31.5 km/hr
  • C. 33 km/hr
  • D. 34 km/hr
  • Discuss
  • 10. From a point P on a level ground, the angle of elevation of the top of a tower is 30°, if the tower is 100 m high, find the distance of point P from the foot of the tower.

  • Options
  • A. 100 m
  • B. 173 m
  • C. 200 m
  • D. 273 m
  • Discuss

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