Question

$\huge \fbox \red{❥ Question}$


Two poles of equal heights are standing opposite each other on either side of the road, which is 80 m wide. From a point between them on the road, the angles of elevation of the top of the poles are 60° and 30°, respectively. Find the height of the poles and the distances of the point from the poles.


(REQUIRED QUALITY ANSWER)​

Answer 1

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

Step-by-step explanation:

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