Question

Two poles of equal heights are standing on either side of the road; which is 80 m wide. From a
point between two poles on the road angle of elevtion of the tops of poles are 60° and 30°
respectively. Find the height of the poles and distance of the point from poles.​

Answer 1

Width of road is 90 ft

Heights of the pole are in the ratio 1 : 2

Angle of elevation of poles = 60°

Heights of the poles

→ Let the height of AB be x

→ Let the height of ED be 2x

→ Let CD = y, BC = 90 - y

→ Consider Δ ABC

 

 

 

 x = ( 90 - y) √3

→ Consider Δ EDC

   

 

 

→ The LHS of equation 1 and 2 are equal. Therefore RHS must also be equal.

   

→ Cancelling x on both sides,

   

 y = 180 - 2y

 3y = 180

   y = 60

→ Substitute the value of x in equation 2

 √3 = 2x/60

60√3 = 2x

→ Hence height of ED = 2x = 60√3 ft

→ Height of AB = x = (60√3)/3 = 30√3 ft