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.
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Step-by-step explanation:
HEIGHTS AND DISTANCE
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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.
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