What will be the Height of Tower?If

The shadow of a tower standing on a level plane is found to be 40m longer when the sun’s altitude is 45o than when it is 60o. The height of the tower is:

  1. 30(3+sqrt. 3)m
  2. 40 (3+sqrt. 3)m
  3. 10(3+sqrt. 3)
  4. 20 (3+sqrt. 3) m
Monis Rasool Professor Asked on 8th July 2015 in Maths.
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    Answer:(4) (4) 20(3 + Ö3).
    Explanation:-
    In the figure- 

    RE: What will be the Height of Tower?If


    Let PQ be the height of the tower is h m and QR be its shadow of length x m when the sun’s altitude is 60o.
    And QS be the length of the shadow, when the angle of elevation is 30o.
    According to the question,
    QS is 40 m longer than QR.

    Therefore, QS = (40 + x) m
    Now, in the right triangle ABC,
    tan60o = PQ/QR
    Therefore, Ö3 = h/x                                            { tan60o = Ö3}
    Then, h = xÖ3                 …………………………….. (1)
    In right triangle PQS,
    tan45o = PQ/QS
    Therefore, 1 = h/(x + 40)                               {tan45o = 1}
    h = (x + 40)                ………………….. (2)
    From equation (1) & (2),
    xÖ3 = (x + 40)
    xÖ3 = x + 40
    xÖ3 = x + 40
    xÖ3 – x = 40
    x(Ö3 – 1) = 40
    x = 40/(Ö3 – 1)
    h = 40 x Ö3/(Ö3 – 1)                      { From equation (1) }
    h = 40Ö3(Ö3 + 1)/( Ö3 – 1)( Ö3 + 1)
    h = {40Ö3 x Ö3 + 40Ö3}/(3 – 1)                                            {a2 – b2 = (a + b)(a – b)}
    h = {40 x 3 + 40Ö3}/2
    h = 20(3 + Ö3)
    Hence, the answer is (4) 20(3 + Ö3).

    Anurag Mishra Professor Answered on 8th July 2015.
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