Two poles of equal heights are standing opposite each other on either side of the road, which is 80 m wide. From a point between them on the road, the angles of elevation of the top of the poles are 60° and 30°, respectively. Find the height of the poles and the distances of the point from the poles.
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Answer:
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>>Two poles of equal heights are standing
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Two poles of equal heights are standing opposite to each other, on either side of the road, which is 80m wide. From a point between them on the road, the angles of elevation of top of the poles are 60
o
and 30
o
respectively. Find the height of the poles.
Medium
Solution
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Given that:
∠APB=60
∘
,∠CPD=30
∘
,AC=80m
To find:
The height of the pole=AB=CD=?
Solution:
Let AB and CD be the two poles of equal height and P be the point on the road between the poles.
In △APB,
tan60
∘
=
AP
AB
or, AP=AB×
tan60
∘
1
or, AP=
3
AB
−−−−−−−(i)
In △PCD,
tan30
∘
=
CP
CD
or, CP=CD×
tan30
∘
1
or, CP=
3
CD=
3
AB ∵AB=CD −−−−−−−(ii)
Adding eqn. (i) and eqn. (ii) we get,
AP+CP=
3
AB
+AB
3
or, AC=AB(
3
+
3
1
)
or, 80m=4
3
AB
or, AB=20
3
m
Therefore, height of the pole=20
3
m=34.64m