Question

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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.

Answer 2

Answer:

,

Step-by-step explanation:

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