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Question

A vertical pole of length 7.5 m casts a shadow 5 m long on the ground and at the same time a tower casts a shadow 24 m long. Find the height of the fower.

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Solution

The height of the pole = 7.5 m
length of pole of shadow = BC = 5 m
Length of shadow of tower = EF = 24 cm

Height of tower, ie, ED = ?

in ΔABC and ΔDEF,

B=E=90o (Both 90o as both are vertical to ground)

C=F ( Same elevation in both cases as both the sahdows are cast at the same time)

ΔABCΔDEF (AA similarity criterion)

We know that if two triangles are similar, ratio of their sides are in proportion,

so, ABDE=BCEF7.5DE=524DE=24×7.55=36 m

Height of the tower = 36 m


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