A man is standing on a corner of a square field He observes that the angle of elevation of the top o...........

Quantitative Aptitude ( CCS) Trignometry

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.

100m²

2500m²

1600m²

1200m²

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Explanation:

Let ABCD is the square field, the person is standing at A and the tower is CE.
Heights & Distance Probs
Here ∠CAE = 60⁰
Let the person moves to the point F such that AF = 100√2m and ∠CFE = 30⁰
Now in ΔACE tan 60⁰ = CE/AC
⇒ CE = √3AC ----(1)
In ΔECF, tan 30⁰ = EC/CF

Equating (1) & (2) we get

⇒ 3AC = 100√2m + AC
⇒ 2AC = 100√2m
⇒ AC = 50√2m
Since AC is the diagonal of the square,
so the side of the square is 50m.
Hence the area of the square field is (50)² = 2500m².