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

Solution:

Given, a 15 m high tower casts a shadow of 24 m long.

A telephone pole casts a shadow of 16 m long.

We have to find the height of the telephone pole

Let h be the height of the telephone pole.

In triangle ADC,

By Pythagorean theorem,

tan θ = opposite / adjacent

So, tan θ = CD/AC

tan θ = 15/24 ------------------- (1)

In triangle ABE,

By Pythagorean theorem,

tan θ = EB/AB

tan θ = h/16 ---------------------- (2)

Equating (1) and (2),

h/16 = 15/24

h/16 = 5/8

h = 16(5)/8

h = 2(5)

h = 10 cm

Therefore, the height of the telephone pole is 10 cm.

✦ Try This: A 20 metres high tower casts a shadow 36 metres long at a certain time and at the same time, a telephone pole casts a shadow 18 metres long. Find the height of the telephone pole

☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 6

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NCERT Exemplar Class 10 Maths Exercise 6.3 Problem 14

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

Summary:

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. The height of the telephone pole is 10 cm

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