Anaircraft is flying at a height of 3400m above theground . 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 ?

Anaircraft is flying at a height of 3400m above theground . If the ang

1.	Anaircraft is flying at a height of 3400m above theground . 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 ?
Answer» Solution :Infig, O is the observation point at the ground, A and B are the positions of aircraftfor 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)` .