Question

two poles of equal heights are standing oposite to each other oneither side of the road which is 120 feet wide from a point between them on the road, the angles of elevation of the top of the poles are 60 degrees and 30 degrees respectively find the height of the poles and the distences of the point from the poles?

Answer 1

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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Answer 2

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