A vertical pole of 10 m casts a shadow of 8 m at certain time of the day. What will be the length of the shadow cast by a tower standing next to the pole, if its height is 110 m?

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Solution

Let the height of the pole be AB = 10 m and the length of its shadow be BC = 8 m.

Let the height of the tower be PQ = 110 m and the length of its shadow be QR = x.

In ΔABC and ΔPQR:

∠B = ∠Q (90°)

∠C = ∠R (Elevation of the sun at the same time of the day is same for the pole and the tower)

∠A = ∠P (Angle sum property)

Thus, ΔABC and ΔPQR are equiangular.

∴ ΔABC ||| ΔPQR

Hence, the length of the shadow cast by the tower is 88 m.

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