Question

Two poles of equal height are standing opposite to each other on the either side of the road which is 80 m wide. From a point P b/w then on road , the angle of elevation of the top of a pole is 60°and the angle of depression from the top of another pole at point P is 30°. Find the heights of the polesand distances of the point P from the poles.

Answer 1

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Answer 2

Here is your solution

Given:-

AB and CD be the two poles of equal height.

Their heights be H m.

BC be the 80 m wide road.

P be any point on the road.

Let ,
CP be x m,

BP = (80 – x) . 
Also, ∠APB = 60° and ∠DPC = 30°

In right angled triangle DCP, 

Tan 30° = CD/CP 
⇒ h/x = 1/√3 
⇒ h = x/√3 ---------- (1) 

In right angled triangle ABP

Tan 60° = AB/AP 
⇒ h/(80 – x) = √3
⇒ h = √3(80 – x) 
⇒ x/√3 = √3(80 – x) 
⇒ x = 3(80 – x) 
⇒ x = 240 – 3x
⇒ x + 3x = 240
⇒ 4x = 240
⇒ x = 60 

Height of the pole, h = x/√3 = 60/√3 = 20√3. 

Thus, position of the point P is 60 m from C and height of each pole is 20√3 m.

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