# Two Poles of Equal Heights Are Standing Opposite Each Other on Either Side of the Road, Which is 80 M Wide. from a Point Between Them on the Road - Mathematics

Theorem

Two poles of equal heights are standing opposite each other on either side of the road, which is 80 m wide. From a point between them on the road, the angles of elevation of the top of the poles are 60° and 30° respectively. Find the height of the poles and the distances of the point from the poles.

#### Solution

Let the poles be ab, CD each of height h meter and E is the point between the poles on the road

Let ∠AEB = 60°; ∠CED = 30° and DE be x meter.

BE = (80 - x) m

In ΔAEB,

tan 60° = "AB"/"BE"

=> sqrt3 = "h"/(20 - "x")

=> "h" = sqrt3(80 - "x") m...(i)

In ΔCDE, tan 30 = "CD"/"DE"

=> 1/sqrt3 = "h"/"x"

=> "h" = "x"/sqrt3 "m"....(ii)

From equation (i) and (ii) we get

"x"/sqrt3 = sqrt3(80 - "x")

=> x = 240 - 3x

=> 4x = 240

=> x = 60 m

Put value of x in equation (ii) we get

H = 20sqrt3m, DE = 60m and BE = 20m

Hence, the height of each pole is 20sqrt3m and distance of the point from the poles are 60 m and 20 m.

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