Question

Two poles of equal heights r standing opposite you each other on either side of the road which is 80 m wide . From a point between them on the road the angles of elevationof the top of the poles are 60. and 30 .respectively. find the height of the poles and the dinstance of the points 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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