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The angle of elevation of the summit of a mountain from a point on the ground is $45^{0}$ . After climbing up one km towards the summit at an inclination of $30^{0}$ from the ground, the angle of elevation of the summit is found to be $60^{0}$ . Then the height (in km) of the summit from the ground is

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$\frac{1}{\sqrt{3} - 1}$

$\frac{\sqrt{3} + 1}{\sqrt{3} - 1}$

$\frac{1}{\sqrt{3} + 1}$

$\frac{\sqrt{3} - 1}{\sqrt{3} + 1}$

answer is C.

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Detailed Solution

$\Rightarrow \sqrt{3} = \frac{h - 1 / 2}{h - \sqrt{3} / 2} \Rightarrow \sqrt{3} h - \frac{3}{2} = h - \frac{1}{2} \Rightarrow (\sqrt{3} - 1) h = 1 \Rightarrow h = \frac{1}{\sqrt{3} - 1}$

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