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Question

A vertical stick 12 m long casts a shadow 8 m long on the ground. At the same time, a tower casts a shadow of length 40 m on the ground . Determine the height of the tower.

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Solution

Let AB represent the height of the vertical stick and PQ represent the height of the tower.

Given: AB=12 m , BC=8 m and QR=40 m

In ABC and PQR,ABC=PQR [90° each]ACB=PRQ [Angle of elevation would be same for both the cases ]Therefore, by AA similarity test, ABC ~ PQRHence, ABPQ=BCQR=CARP [Corresponding sides of similar triangles ]Considering ABPQ=BCQR12PQ=840PQ=12×408=60 m

Therefore, the height of the tower is 60 m .

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