Question

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

Answer 1

$\textbf{Answer is in Attachment !}$

Answer 2

Answer:

Solution

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.