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 ${60}^{\circ }$ and ${30}^{\circ }$. 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

$tan{60}^o=\frac{AB}{AP}$

$=\sqrt{3}=\frac{h}{x}$

$=\sqrt{3}x=h$.....................1

In triangle PCD , we have

$tan{30}^o=\frac{CD}{CP}$

$=\frac{1}{\sqrt{3}}=\frac{h}{150-x}$

$=h\sqrt{3}=150-x$....................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