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An aircraft is flying at a height of 34...

An aircraft is flying at a height of 3400 m above the ground . If the angle subtended at a ground observation point by the air-craft positions 10 . 0 s apart is `30^(@)` , what is the speed of the aircraft ?

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In fig, O is the observation point at the ground, A and B are the positions of aircraft for which `angle(AOB) = 30^(@)` . Draw a perpendicular OC on AB . Here OC = 3400 m and `angle(AOC) = angle(COB) = 15^(@)` . Time taken by aircraft from A to B is 10 s .
In `Delta AOC , AC = OC tan 15^(@) = 3400 xx 0 . 2679 = 910 . 86` m
AB + AC + CB = AC + AC = 2 AC
` = 2 xx 910 . 86` m
Speed of the aircraft, v `= ("distance " AB)/("time")`
` = (2 xx 910 . 86)/(10) = 182 . 17 ms^(-1) = 182 . 2 ms^(-1)` .
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