Question

Two poles of equal heights are standing opposite each other on either side of the roads, 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.​

Answer 1

Answer:

The values we have,

AB = 80 cm

AC = BD = h

AP = x and BP = 80 - x

→ Perpendicular/Base = tan∅

→ AC/AP = tan 30°

→ AC/x = 1/√3

→ AC = x/√3

→ BD/BP = tan 60°

→ BD/(80 - x) = √3

→ BD = √3(80 - x)

Since, AC = BD

→ x/√3 = √3(80 - x)

→ x = 240 - 3x

→ 4x = 240

→AP = x = 60

So, BP = (80 - 60) = 20

→ AC = 60/√3

→ AC = 60√3/3

→ AC = BD = 20√3

Answer

Height of both poles is 20√3 m and point is 60 m away from left pole and 20 m away from right pole.

Answer 2

The values we have,

AB = 80 cm

AC = BD = h

AP = x and BP = 80 - x

→ Perpendicular/Base = tan∅

→ AC/AP = tan 30°

→ AC/x = 1/√3

→ AC = x/√3

→ BD/BP = tan 60°

→ BD/(80 - x) = √3

→ BD = √3(80 - x)

Since, AC = BD

→ x/√3 = √3(80 - x)

→ x = 240 - 3x

→ 4x = 240

→AP = x = 60

So, BP = (80 - 60) = 20

→ AC = 60/√3

→ AC = 60√3/3

→ AC = BD = 20√3