A man is standing on a corner of a square field. He observes that the angle of elevation of the top of a pole in the corner just diagonally opposite to this corner is 600. When he moves 100√2m from the corner along the same straight line (along the diagonal joining the two corners in question), he finds that the angle is 300. Find the area of the field.
Answers
Given : A man is standing on a corner of a square field. He observes that the angle of elevation of the top of a pole in the corner just diagonally opposite to this corner is 60°. When he moves 100√2m from the corner along the same straight line . he finds that the angle is 30°
To find : area of the field.
Solution:
Let say height of pole = h m
& diagonal length = d m
angle of elevation = 60°
Tan 60° = h /d
=> h = d√3
after moving 100√2m
angle of elevation = 30°
Tan 30° = h /(d-100√2)
=> 1/√3 = d√3/(d-100√2)
=> d - 100√2 = 3d
=> 2d = 100√2
=> d = 50√2
Diagonal of square = side√2
=> Side of the Square = 50 m
Area of the square field = 50² = 2500 m²
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