Question

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 45∘ and 30∘. Find their height and position of the point.

Answer 1

Step-by-step explanation:

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

tan60o=APAB

=3=xh

=3x=h.....................1

In triangle PCD , we have 

tan30o=CPCD

=31=150−xh

=h3=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