# 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

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Answer:(4) (4) 20(3 + Ö3).
Explanation:-
In the figure-

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.