Two poles of equal heights are standing opposite each other on either
side of the road which is 80m wide. From a point O between them on the
road, the angles of elevation of the top of the poles are 600
and 300
respectively. Find the height of the poles and the distances of the point
from the poles.
Answers
Answered by
2
Answer:
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
Similar questions