Two poles of equal height stand vertically opposite to each other on either side of the road, which is 100 m wide. From a point on the road between the poles, the angle of elevation of the tops of the poles are 30 degree and 60 degree . Find the heights of the poles. Also find the distance of the point from the feets to the poles.
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Answer:
In △AOC,
tan60
o
=
x
h
∴x=
3
h
In △BOD,
tan30
o
=
100−x
h
3
1
=
100−x
h
100−x=h
3
100−h
3
=x x=
3
h
∴100−h
3
=
3
h
∴h=25
3
m
∴x=
3
h
=
3
25
3
∴x=25 m
∴OC=25 m and OD=75 m.
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