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Question

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 :


A
13+1
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B
3+131
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C
313+1
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D
131
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Solution

The correct option is D 131

If ΔCDF
sin30=z1z=12km
cos30=y1y=32km
Now in ΔABC
tan45=hx+yh=x+y
x=h32
Now in ΔBDE
tan60=hzx
3x=h12
3(h32)=h12h=131km






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