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Sum

A 15 metres high tower casts a shadow 24 metres long at a certain time and at the same time, a telephone pole casts a shadow 16 metres long. Find the height of the telephone pole.

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#### Solution

Let BC = 15 m be the tower and its shadow AB is 24 m.

At that time ∠CAB = 8, Again, let EF = h be a telephone pole and its shadow DE = 16 m.

At the same time ∠EDF = 8

Here, ΔASC and ΔDEF both are right-angled triangles.

In ΔABC and ΔDEF,

∠CAB = ∠EDF = θ

∠B = ∠E ......[Each 90°]

∴ ΔABC ∼ ΔDEF ......[By AAA similarity criterion]

Then, `(AB)/(DE) = (BC)/(EF)`

⇒ `24/16 = 15/h`

∴ h = `(15 xx 16)/24` = 10

Hence, the height of the telephone pole is 10 m.

Concept: Similarity of Triangles

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