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

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

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Let AB be the vertical stick and BC be its shadow.

Given:

AB = 7.5 m, BC = 5 m

Let PQ be the tower and QR be its shadow.

Given:

QR = 24 m

Let the length of PQ be x m.

In ∆ ABC and ∆ PQR, we have:

∠ABC = ∠PQR = 90°

∠ACB = ∠PRQ (Angular elevation of the sun at the same time)

Therefore, by AA similarity theorem , we get :

∆ ABC ~ ∆ PQR

⇒ AB/BC = PQ/QR

⇒ 7.5/5 = x/24

x = 7.5/5 x 36 cm

Therefore, PQ = 36 m

Hence, the height of the tower is 36 m.