Q.

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

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a

13−1

b

13+1

c

3−13+1

d

3+13−1

answer is A.

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Detailed Solution

In ΔBCDCDS in B=BCSinD∣ ⇒1Sin15°=BCSin150°⇒BC=23-1 In ΔABC,Sin45°=ABBC⇒AB=23-1·12=13-1
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The angle of elevation of the summit of a mountain from a point on the ground is 45°.  After climbing up one km towards the summit at an inclination of 30° from the ground, the angle of elevation of the summit is found to be 60°. Then the height (in km) of the summit from the ground is: