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Question

The shadow of a tower standing on a level ground is found to be 60 m longer when the Sun’s altitude is 30 than when it is 60. Find the length of the shadow at 30.



Your Answer
A

40 m

Your Answer
B

50 m

Your Answer
C

60 m

Correct Answer
D

90 m


Solution

The correct option is D

90 m


In the above figure, 

Let BD is the length of the shadow when sun is at 60°  be x m

AB is the length of the shadow when sun is at 30° be (x + 60) m 

AD = 60 m 

In ΔABC,

tan30=BCAB

BC3=AB

i.e. BC=AB3= 60+x3  -------(i)

In ΔBCD,

tan60=BCBD 

BC=BD 3

BC=x 3  ---------(ii)

Equating equation (i) and (ii), we get

60+x3=x3

 2x = 60 

 x = 30

Hence, length of the shadow = (x + 60) m = 90 m 

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