A flag - staff of 5 meters high stands on a building of 25 meters...

A flag - staff of

5

meters high stands on a building of

25

meters height. For an observer at a height of

30

meters,& the flag-staff and the building subtend equal angles. The distance of the observer from the top of the flag - staff is A flag - staff of 5 meters high stands on a building of 25 meters height. For an observer at a height of 30 meters,&

A flag - staff of 5 meters high stands on a building of 25 meters height. For an observer at a height of 30 meters,&

Options

A $\dfrac{5\sqrt{3}}{2}\text{m}$
B $5\sqrt{\dfrac{3}{2}}\text{m}$
C $5\sqrt{\dfrac{2}{3}}\text{m}$
DNone of these

Correct answer

B. $5\sqrt{\dfrac{3}{2}}\text{m}$

Step-by-step solution

We have

tan \alpha = \dfrac{5}{x}

and

\tan 2\alpha = \dfrac{30}{x}

∴\tan 2\alpha = \dfrac{30}{5cot \alpha} ⇒ \tan 2\alpha = 6tan \alpha

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