A vertical pole of length 5m casts a shadow 2m long on the ground and at the same time a - Maths -

Question

A vertical pole of length 5m casts a shadow 2m long on the
ground and at the same time a tower casts a shadow 9m long Find the
height of the tower

Lalit Mehra · Accepted Answer

AB is the pole and BC is the shadow of pole.

Given, AB = 5 m and BC = 2 m.

PQ is the tower and QR is the shadow of tower.

Given, QR = 9 m

Let the height of tower be h m.

Since the length of shadow of pole and tower area measured at the same times, so the angle of elevation of source of light for both is same at that moment of time.

∴ ∠C = ∠R

In ΔABC and ΔPQR,

∠B = ∠Q (90°)

∠C = ∠R

∴ ΔABC $≅$ ΔPQR (AA similarity)

$\Rightarrow \frac{AB}{PQ} = \frac{BC}{QR} (Corresponding sides are proportional) \Rightarrow \frac{5 m}{h m} = \frac{2 m}{9 m} \Rightarrow h = \frac{45}{2} m = 22.5 m$

Thus, the height of tower is 22.5 m.

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A vertical pole of length 5m casts a shadow 2m long on the ground and at the same time a tower casts a shadow 9m long. Find the height of the tower.