Question

Two poles of equal height are standing opposite to each other on the other side of the road which is 80 m wide from the point in between them on the road the angle of elevation of the top of the polar 60 degree and 30 degree respectively find the height of pole and distance of the point from the pole

Answer 1

Let AB and CD be the two poles of equal height and their heights be

H m. BC be the 80 m wide road. P be any point on the road. Let CP

be x m, therefore BP = (80 – x) .

Also, ∠APB = 60° and ∠DPC = 30°

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

height = 20√3
distance= 20, 60