Question

Two poles of equal heights are standing opposite to each other on either side of the road,
which is 120 feet 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.
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Answer 1

Answer:

Step-by-step explanation:

From ΔABD,

Tan30° = AD/BD = h/x

=> h = xTan30° = x/√3

From ΔCDE,

Tan60° = EC/ED = h/120-x

h = (120 - x)Tan60°

  = (120 - x)√3.

Since heights of both poles are equal

x/√3 = (120 - x)√3.

=> 3x = 120 -x

=> 4x = 120

=> x= 30 feet.

Thus the distance of the point is 30 feet from Pole AB.

Height of pole = 30/√3 = 30√3/3 = 10√3 feet.

Answer 2

Step-by-step explanation:

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