Question

Two poles of equal heights are standing opposite to each other on either side of a road, which is 80m

wide. From a point between them on the road, angles of elevation of their top are 30° and 60°. Find the

heights of the poles and distance of point from poles.​

Answer 1

Step-by-step explanation:

let say the point is x m distance from one pole

automatically it will be (80-x) m from another pole

so

one angle 30 and another 60

let say for 30 it will be x and (80-x) will be 60

using tan ratios

tan30 =h/x

h= xtan30 = x/√3 ---eq1

tan60= h/(80-x)

h = (80-x) *√3---eq2

from eq1 and 2

(80-x) *√3=x/√3

x= 3(80-x)

x= 240-3x

4x= 240

x= 240/4= 60

so x= 60m and (80-x) = 80-60=20m

now height = x/√3= 60/√3 = 20√3