Question

Vijay is trying to find the average height of a tower
near his house. He is using the properties of similar
triangles. The height of Vijay's house is 20 m when
Vijay's house casts a shadow 10 m long on the
ground. At the same time, the tower casts a
shadow 50 m long on the ground. At the same time,
the house of Ajay casts 20 m shadow on the
ground

Answer 1

Given:

The height of Vijay's house is 20 m when  Vijay's house casts a shadow 10 m long on the  ground.

At the same time, the tower casts a  shadow 50 m long on the ground

He is using the properties of similar  triangles

To find:

The average height of a tower  near his house

Solution:

Let's assume,

"AB" → the height of Vijay's house = 20 m

"BC" → the length of the shadow of Vijay's house = 10 m

"PQ" → the height of the tower

"QR" → the length of the shadow of the tower = 50 m

Consider ΔABC and ΔPQR, we have

∠ABC = ∠PQR = 90° ..... [both Vijay;s house and the tower are vertical to the ground]

∠ACB = ∠PRQ ..... [since the shadows are cast at the same time ∴ the angle of elevation of the sun is the same in both the cases]

∴ Δ ABC ~ Δ PQR .... [By AA similarity]

We know that,

The corresponding sides of two similar triangles are proportional to each other

∴ $\frac{AB}{PQ} = \frac{BC}{QR}$

on substituting the values of AB, BC & QR, we get

$\implies \frac{20}{PQ} = \frac{10}{50}$

$\implies \frac{20}{PQ} = \frac{1}{5}$

$\implies PQ = 20 \times 5$

$\implies \bold{PQ = 100\:m}$

Thus, the average height of the tower near Vijay's house is → 100 m.

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Also View:

A vertical row of trees 20 m long casts a shadow 16 m long on the ground. At the same time a tower

casts the shadow 48 m long on the ground.

(1) Determine the height of the tower

fit) Which mathematical concept is used in this problem?​

https://brainly.in/question/14367276

The ratio of the height of a tower and the length of its shadow on the ground is√3:1 what is the angle of elevation of the sun

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