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A flag staff of height $h$ stands in the centre of a rectangular field and subtends angle of $15^{o}$ and $45^{o}$ at the midpoint of its sides. Find the distance between them.

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h \sqrt{2 + \sqrt{3}}

2 h \sqrt{2 + \sqrt{3}}

4 h \sqrt{2 + \sqrt{3}}

3 h \sqrt{2 + \sqrt{3}}

answer is B.

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Detailed Solution

It is given that a flag staff of height

h

stands in the centre of a rectangular field and subtends angle of

15^{o}

and

45^{o}

at the midpoint of its sides.
Question Image

In △ POE,

\tan 15^{\circ} = \frac{h}{OE}

⇒

OE = \frac{h}{2 - \sqrt{3}} . . . . (\tan 15^{\circ} = 2 - \sqrt{3})

In △ POF,

\tan 4 5^{\circ} = \frac{h}{OF}

⇒

OF = \frac{h}{\tan 45^{\circ}} = h

In △ OEF,
By pythagoras theorem,

EF = \sqrt{O E^{2} + O F^{2}}

⇒

EF = h \sqrt{{(\frac{1}{2 - \sqrt{3}})}^{2} + 1}

⇒

EF = h \sqrt{{(\sqrt{3} + 2)}^{2} + 1}

⇒

EF = h \sqrt{2 + \sqrt{3}}

m
Hence, the correct option is 1.

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