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Home Aptitude Height and Distance See What Others Are Saying!
  • Question
  • 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

  • Correct Answer
  • 273 m 

    Explanation
    Let AB be the lighthouse and C and D be the positions of the ships.

    Two ships are sailing in the sea on the two sides of a lighthouse. The angle of elevation of the top

    Then, AB = 100 m, ∠ACB = 30° and ∠ADB = 45°.

    AB = tan 30° = 1     ⟹     AC = AB x √3 = 100√3 m.
    AC √3

    AB = tan 45° = 1     ⟹     AD = AB = 100 m.
    AD

    ∴ CD = (AC + AD) = (100√3 + 100) m
    = 100(√3 + 1)
    = (100 x 2.73) m
    = 273 m.

  • More questions

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      If log 10 (10x) = 2.7532, then log 10 (10000x) is?

    • Options
    • A. 4.7532
    • B. 5.7532
    • C. 3 x 2.7532
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    • Discuss
    • 2. 
      We have an angle of 2 / 2 .How big it will look through a glass that magnifies things three times?

    • Options
    • A. 2 1° × 4 2
    • B. 2 1° × 3 2
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    • 3. 
      A 200 m long train is running at a speed of 60 km/ hr. Find out the time it takes to pass a man standing at the platform

    • Options
    • A. 10 sec
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    • 4. 
      The rate of interest for the first 2 years is 5% for the next 3 years is 8% and beyond this. It is 10% per annum. If the simple interest for 8 years is Rs . 1280. What is the principal?

    • Options
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    • 5. 
      A pillar 14 cm in diameters is 5 m high. How much material was used to construct it?

    • Options
    • A. (77 x 102)cm3
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    • 6. 
      The price of a product is increased by 20%. If the original price is Rs. 300, what is the final price of the product?

    • Options
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    • Options
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    • 9. 
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    • Options
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