Two pillars of equal heights are standing opposite each other on either side of a road, which is 80m wide. The angles of elevation of the top of the pillars are 60 o and 30° at a point on the road between the pillars. Find the position of the point between the pillars and the height of each pillar
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10th
Maths
Some Applications of Trigonometry
Heights and Distances
Two pillars of equal height...
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Asked on December 20, 2019 by
Satvik Gondhalekar
Two pillars of equal heights stand on either side of a road which is 150 m wide. At a point on the road between the pillars, the angles of elevation of the tops of the pillars are 60
∘
and 30
∘
. Find the height of each pillar and the position of the point on the road.
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Let AB and CD be two pillars ,each of height hmetres.
Let P be a point on the road such that AP=xm. Then,CP =(150−x)m
In triangle PAB , we have
tan60
o
=
AP
AB
=
3
=
x
h
=
3
x=h.....................1
In triangle PCD , we have
tan30
o
=
CP
CD
=
3
1
=
150−x
h
=h
3
=150−x....................2
Eliminating h between eq. 1 and 2, we get
3x=150−x
=x=37.5
Substituting x=37.5 in eq.1 we get ,
h=64.95
Thus the required point is at the distance of 37.5 m from the first pillar and 112.5 m from the second pillar.
The height of the pillars is 64.95 m
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