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Two poles of equal heights are standing opposite to each other on either side of a road, which is $100$ m wide. From a point between them on the road, the angles of elevation of their tops are $30 °$ and $60 °$ . The height of each pole is :

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44

43.25

50

40.5

answer is B.

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Detailed Solution

It is given that two poles of equal heights are standing opposite to each other on either side of a road, which is

100

m wide.
The angles of elevation of their tops are

30 °

and

60 ° .

We have to find the height of each pole
We use

tanθ = \frac{perpendicular}{base}

.
Now, let us consider that

AB

and

CD

be the two poles and

M

be the point where the angle of elevation is made of

30^{0}

and

60^{0}

.
Let the road

CM

= x

m
and

AM

= (100 - x)

In right angled

△ MCD

\tan 60^{0} = \frac{DC}{CM}

\Rightarrow \sqrt{3} = \frac{h}{x}

[since

\tan 60^{0} = \sqrt{3}

]

\Rightarrow h = x \sqrt{3} \dots \dots \dots

(i)
In right angled

△ MAB

\Rightarrow \tan 30^{0} = \frac{BA}{AM}

\Rightarrow \frac{1}{\sqrt{3}} = \frac{h}{100 - x}

[since

\tan 30^{0} = \frac{1}{\sqrt{3}}

]

\Rightarrow h \sqrt{3} = 100 - x

\Rightarrow (x \sqrt{3}) \sqrt{3} = 100 - x

.... (From {i})

\Rightarrow 3 x = 100 - x

\Rightarrow 4 x = 100

\Rightarrow x = 25

m
Let the height of pole

CD

\Rightarrow CD = 25 \times 1.732

\Rightarrow CD = 43.25

m
Thus, height of each pole is

43.25

m.
Therefore, the correct option is 2.

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