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 60 and 30 . Find the distance of the point from the two poles.

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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.

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

Hence the point is 20 m from one pole and 60 meters from the other pole.





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