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A person standing on the ground observes the angle of elevation of the top of a tower to be $30 °$ . On walking a distance one unit in a certain direction he finds the elevation of the top to be the same as before. He then walks a distance $\frac{5}{3}$ unit at right angles to his former direction, and finds that the elevation of the top has doubled. The height of the tower can be

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$\sqrt{\frac{5}{16}}$

$\sqrt{\frac{85}{48}}$

$\sqrt{\frac{6}{5}}$

$\sqrt{\frac{48}{85}}$

answer is B.

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Detailed Solution

Let H be height of the tower ${(\sqrt{{(\sqrt{3} H)}^{2} - \frac{1}{4}} - \frac{5}{3})}^{2} + \frac{1}{4} = \frac{H^{2}}{3}$

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