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Question

The angles of elevation of the top of a vertical tower from two points. 30 metros apart, and on the same straight line passing through the base of tower, are 300 and 600 respectively. The height
of the tower is

A
10 m
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B
15 m
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C
153
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D
30 m
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Solution

The correct option is C 153
Let AB is tower, the angles of elevation of the top of a vertical tower AB from two points D and C are 300 and 600 respectively.
Let the height of tower be h metres
and BC=xm
In triangle ABC,ABBC=tan600
hx=3...........(i)
In triangle ABD,ABBD=tan300
h(x+30)=13
or 3h=x+30
Put value of x from equation Ci) in equation (ii), we get
3h=h3+30
or 3hh3=30
or 2h3=30
h=3032=153
So, height of the tower is 153metre.
84169_97042_ans.jpg

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