jee-main 2020 Q59

jee-main · India · session2_06sep_shift2 Sine and Cosine Rules Heights and distances / angle of elevation problem
The angle of elevation of the summit of a mountain from a point on the ground is $45^{\circ}$. After climbing up one km towards the summit at an inclination of $30^{\circ}$ from the ground, the angle of elevation of the summit is found to be $60^{\circ}$. Then the height (in km) of the summit from the ground is:
(1) $\frac{\sqrt{3}-1}{\sqrt{3}+1}$
(2) $\frac{\sqrt{3}+1}{\sqrt{3}-1}$
(3) $\frac{1}{\sqrt{3}-1}$
(4) $\frac{1}{\sqrt{3}+1}$ 
The angle of elevation of the summit of a mountain from a point on the ground is $45^{\circ}$. After climbing up one km towards the summit at an inclination of $30^{\circ}$ from the ground, the angle of elevation of the summit is found to be $60^{\circ}$. Then the height (in km) of the summit from the ground is:\\
(1) $\frac{\sqrt{3}-1}{\sqrt{3}+1}$\\
(2) $\frac{\sqrt{3}+1}{\sqrt{3}-1}$\\
(3) $\frac{1}{\sqrt{3}-1}$\\
(4) $\frac{1}{\sqrt{3}+1}$
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