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Question

The angle of elevation of the top of an incomplete vertical pillar at a horizontal distance of 100m from its base is 450. If the angle of elevation of the top of complete pillar at the same point is to be 600, then the height of the incomplete pillar is to be increased by :

A
502
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B
100m
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C
100(31)m
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D
100(3+1)m
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Solution

The correct option is C 100(31)m
Let D be the fixed point, AC be the pillar

CD=100m

AB is the height to be increased.

In BCD,tan45=BCDC

1=BCDC=BC100

In ACD,tan60=ACDC

3=AC100

AC=1003m

Height to be increased=AB=ACBC=1003100=100(31)m

to complete the pillar 100(31)m has to be increased.

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