Two hoardings of cleanness are put on a 80m wide road on two poles which are opposite
sides of road and are of some height. The angle of elevation of both pole; from a pointat
theroad is 60' and 30'. Find the height of poles and distance of poles from that point
Answers
Answered by
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Step-by-step explanation:
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
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