Question

Two poles of equal heights are standing opposite each other on either side

of the road, which is 100 m wide. From a point between them on the road,

the angles of elevation of the top of the poles are 60° and 45°, resp.

Find height of the poles and the distances of the point from the poles.
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Answer 1

Step-by-step explanation:

Let AC and BD be two poles of the same height h=m

let AB=100m

let AP=x m, therefore PB=(100-x)m

In a triangleAPC,

tan30°=AC/AP

1/√3=h/x ...1

in triangle BPD,

tan60°=BD/AB

√3=h/100-x.... 2

Dividing (1) by (2),

1/√3/√3 =h/x/h/100-x

1/3=100-x/x

x=300-3x

4x=300

x=75°

From(1),

1/√3=h/x

h=75/√3=43.3012701892

Thus the height of the both the poles is 43.3012701892 and distances of the point from the poles are 75° and 43°

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