Question

The length of the shadow of a 1.5 m high pole at a certain time of the day is 2.5 m. What is the height of another pole whose shadow at that time is 3.5 m long?​

Answer 1

Answer

Given: A person 1.65 m tall casts 1.5 m shadow at the same time a lamppost casts a shadow of 5.4 m

The angle is same as the incident occurred at the same point in time.

So sum makes the same angle of hitting the top of the person and top of the lamp post

Therefore ABC & DEF are similar triangles

so radius at their sides are the same

Then

DE

AB

=

EF

CB

Let EF=x

5.4

1.5

=

x

1.65

⇒ x=

1.5

1.65×5.4

=

1.5

8.91

x=5.94 m

Height of lamp post =PE=5.94 m

Answer 2

$\sf{\huge{\underline{\purple{Given :-}}}}$

• The length of the shadow of a 1.5 m height pole at a certain time of the day is 2.5 m.

$\sf{\huge{\underline{\blue{To\:Find :-}}}}$

• The height of another pole whose shadow at that time is 3.5 m long.

$\sf{\huge{\underline{\pink{Solution :-}}}}$

The height of shadow is 2.5 m by a pole of the length = 1.5 m

For, The shadow of 1 m. The height of pole is = $\dfrac{1.5}{2.5}$

So, For , the length of pole obtaining shadow of length 3.5 m = $\dfrac{1.5}{2.5}$ × 3.5

➝ 0.6 × 3.5

➝ 2.1 m

So, The height of another pole whose shadow at that time is 3.5 m long is 2.1 m .

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