Two poles of equal heights are standing opposite to each other on either side of a road, which is 100 meters wide. From a
point between them on the road, the angles of elevation of their tops are 30ᵒ and 60ᵒ
. Find the position of the point and
also, the height of the poles. ( use 3 = 1.73)
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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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