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Home Aptitude Height and Distance See What Others Are Saying!
  • Question
  • At a point on a level plane a tower subtends an angle ? and a flag-staff a ft. in length at the top of the tower subtends an angle ? . The height of the tower is :


  • Options
  • A. aSin?Cos?/Cos(? + ?)
  • B. aSin?Cos(? + ?)/Sin?
  • C. aCos(? + ?)/Sin?Sin?
  • D. None of these

  • Correct Answer
  • aSin?Cos(? + ?)/Sin? 

    Explanation

    Let us draw a figure as per given question.
    Let OP be the tower of height h (say) and PQ the flag-staff of height a, such that ?OAP = ? and ?PAQ = ?
    In ?OAP use the formula
    Tan? = P/B = Perpendicular distance / Base distance
    ? Tan? = OP/OA
    ? OA = OP Cot?
    Put the value of OP in above equation, we will get
    ? OA = hCot? ................ (1)
    Now from triangle ?OAQ,
    ? Tan(? + ?) = OQ/OA
    ? OA = OQ Cot(? + ?)
    ? OA = (h + a) Cot(? + ?) .............(2)
    from equation (1) and (2), We will get
    ? hCot? = (h + a) Cot(? + ?)
    ? Cot? / Cot(? + ?) = (h + a) / h
    ? Cot? / Cot(? + ?) = h / h + a / h
    ? Cot? / Cot(? + ?) = 1 + a / h
    ? (Cot? / Cot(? + ?)) - 1 = a / h
    ? (Cot? - Cot(? + ?) ) / Cot(? + ?) = a / h
    ? h = aCot (? + ?) / Cot? - Cot(? + ?)
    After converting Cot into Sin and Cos, We will get
    ? h = aSin?Cos(? + ?)/Sin?


  • More questions

    • 1. Two numbers A and B are such that the sum of 5% of A and 4% of B is two-third of the sum of 6% of A and 8% of B. Find the ratio of A : B.

    • Options
    • A. 2 : 3
    • B. 1 : 1
    • C. 3 : 4
    • D. 4 : 3
    • Discuss
    • 2. A train 240 m long passes a pole in 24 seconds. How long will it take to pass a platform 650 m long?

    • Options
    • A. 65 sec
    • B. 89 sec
    • C. 100 sec
    • D. 150 sec
    • Discuss
    • 3. What was the day of the week on 17th June, 1998?

    • Options
    • A. Monday
    • B. Tuesday
    • C. Wednesday
    • D. Thursday
    • Discuss
    • 4. The H.C.F. of two numbers is 11 and their L.C.M. is 7700. If one of the numbers is 275, then the other is:

    • Options
    • A. 279
    • B. 283
    • C. 308
    • D. 318
    • Discuss
    • 5. 
      1872/ ? ? = 234

    • Options
    • A. 324
    • B. 64
    • C. 8
    • D. 256
    • Discuss
    • 6. 
      For every 4 leaps taken by a dog, a cat takes 5 leaps in the same time. But distance covered in 3 leaps of dog is same as that of 4 leaps of cat. Then what is the ratio of speed of dog and cat?

    • Options
    • A. 15 : 14
    • B. 16 :15
    • C. 12 :11
    • D. 10 : 9
    • Discuss
    • 7. 
      A come of height 7 cm and base radius 3 cm is curved from a rectangular block of wood 10 cm x 5 cm x 2 cm. The percentage of wood wasted is?

    • Options
    • A. 34%
    • B. 46%
    • C. 54%
    • D. 66%
    • Discuss
    • 8. 
      1, 9, 25, 49, 81,?

    • Options
    • A. 90
    • B. 135
    • C. 121
    • D. 125
    • Discuss
    • 9. 
      An accurate clock shows the time as 3:00 after hour hand has moved 135°, the time would be?

    • Options
    • A. 7:30
    • B. 6:30
    • C. 8:00
    • D. 9:30
    • Discuss
    • 10. 
      P.V. Narsihma Rao was elected party leader on 29th may, 1991. What was the day of the week?

    • Options
    • A. Tuesday
    • B. Friday
    • C. Wednesday
    • D. Sunday
    • Discuss


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