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  • 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.

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

Answers (1)

Answer : [10 m]

Let BC = 15 m, AB = 24 m in \DeltaABC and \angleA = Q

Again let DE = 16m and \angleEDF = Q in \DeltaDEF

In \DeltaABC and \DeltaDEF

\angle A=\angle D=Q

\angle B=\angle E=90^{o}

We know that if two angles of one triangle are equal to the two angles of another triangle, then the two triangles are similar by the AA similarity criterion.

\therefore \; \; \; \; \; \Delta ABC\sim \Delta DEF

 \text{Then }\frac{AB}{DE}=\frac{BC}{EF}   \text{(corresponding sides are proportional)}

\frac{24}{16}=\frac{15}{h}

h=\frac{15 \times 16}{24}=10

h=10

Hence the height of the point on the wall where the top of the laden reaches is 10 m.

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