Example 6. The distance between two vertical pillars
is 100 m and the height of one of them is double of the
other. The angles of elevation of their tops at the
mid-point of the line joining their feet are
complementary. Find their heights.
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Answer
Let the height of 1
st
pillar CD = h and height of the 2
nd
pillar = 2h
It is given that the distance between two vertical pillars is 100m
Now, In right ΔABX, we have
tan60
∘
=
BE
AB
⇒
3
=
x
2h
⇒x=
3
2h
In the right ΔCDE, we have
tan30
∘
=
DE
CD
⇒
3
1
=
100−x
h
⇒100−x=
3
h
⇒100−
3
2h
=
3
h
⇒100=
3
2h+3h
⇒h=
5
100
3
⇒h=20
3
m
Hence, the height of the 1
st
vertical pole, CD=20
3
m and the height of the 2
nd
vertical pole, AB=2×20
3
=40
3
m
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