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A flagstaff $5$ m high stands on a building $25$ m high. As observed from a point at a height of $30$ m, the flagstaff and the building subtend equal angles. Find the distance of the observer from the top of the flagstaff.

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\frac{5 \sqrt{3}}{2}

5 \sqrt{\frac{3}{2}}

5 \sqrt{\frac{2}{3}}

None of these

answer is B.

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Detailed Solution

It is given that a flagstaff

5

m high stands on a building

25

m high.
From a point at a height of

30

m, the flagstaff and the building subtend equal angles.
Let AB be the building and BC be the flagstaff.
Question Image

OB is the bisector of ∠COA and OA is the bisector of ∠ BOM.

∴ \frac{OC}{OA} = \frac{BC}{AB}

⇒

\frac{x}{\sqrt{x^{2} + 30^{2}}} = \frac{5}{25}

⇒

x = \frac{30}{\sqrt{24}}

⇒

x = \frac{30}{2 \sqrt{6}}

∴ x = 5 \sqrt{\frac{3}{2}}

Hence, the correct option is 2.

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