Question

two pillars of equal height are in either side is the road which is 100m wide. the angles is elevation of the top of the pillars are 60°and 30°at the point on the road between the pillars. find the position is the point between the pillars and the height of each pillar​

Answer 1

Answer.....

ANSWER

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

=root 3=h/x

=root3x=h.....................1

In triangle PCD , we have

tan30 =cd/cp

1/root3=h/150-x

h=root3=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