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  • Question
  • The angle of elevation of an aeroplane as observed from a point 30 m above the transparent water-surface of a lake is 30° and the angle of depression of the image of the aeroplane in the water of the lake is 60°. The height of the aeroplane from the water-surface of the lake is


  • Options
  • A. 60 m
  • B. 45 m
  • C. 50 m
  • D. 75 m

  • Correct Answer
  • 60 m 


  • Height and Distance problems


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    • 1. A helicopter, at an altitude of 1500 m, finds that two ships are sailing towards it, in the same direction. The angles of depression of the ships as observed from the helicopter are 60° and 30°respectively. Distance between the two ships, in metres is

    • Options
    • A. 1000?3
    • B. 1000/?3
    • C. 500?3
    • D. 500/?3
    • Discuss
    • 2. The angles of elevation of the top of a tower from two points at a distance of 4 m and 9 m from the base of the tower and in the same straight line with it are complementary. The height of the tower is

    • Options
    • A. 4 m
    • B. 7 m
    • C. 9 m
    • D. 6 m
    • Discuss
    • 3. A telegraph post is bent at a point above the ground. Its top just touches the ground at a distance of 8?3 m from its foot and makes an angle of 30° with the horizontal. The height (in metre) of the post is

    • Options
    • A. 12
    • B. 16
    • C. 18
    • D. 24
    • Discuss
    • 4. A pilot in an aeroplane at an altitude of 200 m observes two points lying on either side of a river. If the angles of depression of the two points be 45° and 60°, then the width of the river is

    • Options
    • A. (200 + 200/?3) m
    • B. (200 - 200/?3) m
    • C. 400 ?3 m
    • D. (400/?3) m
    • Discuss
    • 5. The angles of elevation of top and bottom of a flag kept on a flag post from 30 metres distance, are 45 and 30 deg respectively. Height of the flag is [taking ?3 = 1.732]

    • Options
    • A. 12 ?3 m
    • B. 15 m
    • C. 14.32 m
    • D. 12.68 m
    • Discuss
    • 6. The angles of elevation of the top of a tree 220 meters high from two points lie on the same plane are 30° and 45°. What is the distance (in metres) between the two points?

    • Options
    • A. 193.22
    • B. 144.04
    • C. 176.12
    • D. 161.05
    • Discuss
    • 7. The angles of elevation of the top of a tower 72 metre high from the top and bottom of a building are 30° and 60° respectively. What is the height (in metres) of building?

    • Options
    • A. 42
    • B. 20?3
    • C. 24?3
    • D. 48
    • Discuss
    • 8. The angle of elevation of an aeroplane from a point on the ground is 45°. After flying for 15 seconds, the elevation changes to 30°. If the aeroplane is flying at a height of 2500 metres, then the speed of the aeroplane in km/hr. is

    • Options
    • A. 600
    • B. 600 (?3 + 1)
    • C. 600 ?3
    • D. 600 (?3 - 1)
    • Discuss
    • 9. A balloon leaves from a point P rises at a uniform speed. After 6 minutes, an observer situated at a distance of 450?3 metres from point P observes that angle of elevation of the balloon is 60 deg. Assume that point of observation and point P are on the same level. What is the speed (in m/s) of the balloon?

    • Options
    • A. 4.25
    • B. 3.75
    • C. 4.5
    • D. 3.45
    • Discuss
    • 10. On walking 100 metres towards a building in a horizontal line, the angle of elevation of its top changes from 45 to 60 deg. What will be the height (in metres) of the building?

    • Options
    • A. 50(3 + ?3)
    • B. 100(?3 + 1)
    • C. 150
    • D. 100?3
    • Discuss


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