Two poles of equal height are standing opposite each other on either side of the
road 80m wide. From a point between them on the road the angles of elevation of
the top of the two poles are respectively 600 and 300
. Find the distance of the point
from the two poles.
Let AB and CD be two poles of height h meters and P be a point between them on the road which is x meters away from foot of first pole AB, PD = (80 - x) meters.
Hence the point is 20 m from one pole and 60 meters from the other pole.
In 🛆ABP , tan `60^0` = `h/x` = h = x`\sqrt{3}` ------------- (1)
In 🛆CDP , tan `30^0` = `h/80 - x` = h = `\frac{80-X}{\sqrt{3}}` ------------- (2)
`x\sqrt{3}` = `\frac{80-X}{\sqrt{3}}`
∵ LHS (1) = RHS (2)
∴ Equating RHS
= 3`x` = 80 -`x`
= 3`x` + `x` = 80
= 4`x` = 80
= `x` = `80/4`
= `x` = 20
∴ 80 - `x` = 80 - 20 = 60 m