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∘.

A

40 m

B

50 m

C

60 m

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 BC√3=AB i.e. BC=AB√3= 60+x√3  -------(i) In ΔBCD, tan60∘=BCBD  BC=BD √3 BC=x √3  ---------(ii) Equating equation (i) and (ii), we get ⇒ 60+x√3=x√3 ⇒ 2x = 60  ⇒ x = 30 Hence, length of the shadow = (x + 60) m = 90 m

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