Question

two poles of equal heights are standing opposite each other on either side of the road the sngle of elevation of the top of the poles are 60 degree and 30 degree, respectively. find the height of the poles and the distances of the point from the poles​

Answer 1

Answer:

Step-by-step explanation:

height of the pole =20√3 m and distance of the point from the polev=20 m and 60 m

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.