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An aircraft is vertically above a point which is 10 km West and 15 km North of a control tower. If the aircraft is 4000 m above the ground, how far is it

from the control tower?


Let us suppose that control tower at the origin(0,0),and ground in the X-Y plane.
hence the directions are considered as (East as +ve X- axis, West as -ve X-axis, North as +ve Y-axis and South as -ve Y-axis)  above Ground as Z-axis.

Therefore position of  the aircraft is P≡(-10,15,4)            --------    (in km)

Distance b/w control tower(O) and aircraft(P) is = OP
OP = √(-10)²+15²+4²) = √341 km 18.46 km  
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