Question

25. Two pillars of equal height 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.

Answer 1

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

solution