Question

Two pillars of equal heights
stand on either side of a roadway asom wide. From a point on
the roadway between the pillars, the angles of elevation of the top of the pillars are 60
and 30° Find the height of the pillars and the position of the point,
Heieht 6 asm, 112,5m from one pillar) plz help ​

Answer 1

Answer:

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

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−x2

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