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An observer standing $50$ m away from a building notices that the angles of elevation of the top and bottom of a flag post on the building are $60^{o}$ and $45^{o}$ respectively. The height of the flag post is?

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50

\sqrt{3}

50

(

\sqrt{3}

+ 1) m

50

(

\sqrt{3}

- 1) m

\frac{50}{\sqrt{3}}

answer is C.

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Detailed Solution

It is given that an observer standing

50

m away from a building notices that the angles of elevation of the top and bottom of a flag post on the building are

60^{o}

and

45^{o}

respectively.
Let

AB

be the building,

BC

be the flag post and

D

be the observer's position. Then,

DA = 50

∠ ADB = 45^{o}

and

∠ ADC = 60^{o}

Now, in △ BAD,

\tan 45^{o}

\frac{AB}{DA}

⇒

1 = \frac{AB}{50}

⇒ AB = 50 m.
And, in △ CDA,

\tan 60^{o}

\frac{AC}{OA}

⇒

\frac{AC}{50} = \sqrt{3}

⇒ AC = 50

\sqrt{3}

m
⇒ BC

= AC - AB

⇒ BC

= 50 \sqrt{3} - 50

Height of the flag post

= 50 (\sqrt{3} - 1)

m
Hence, the correct option is 3.

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