Q. 13

The length of the shadow of a tower standing on level ground is found to be 2x metres longer when the sun's elevation is 30° than when it was 45°. The height of the tower is
A.(2√3x)m

B. ( 3√2x) m

C. (√3 —1)x m

D. (√3 + 1)x m

Answer :


In the above figure, let AB be the tower and BC and BD are the consecutive shadows of AB for two different positions of the sun.


From ∆DBA,



1 = h/y


h = y


or,


DB = BA


Now, from ∆ACB,



or,



On cross multiplying we get,


2x = √3(h+y)


2x + y = √3


2x + h = (√3h)


2x = (√3 – 1)h


x = (√3 – 1)h



h = (√3 + 1)x

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