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

from the control tower.



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Let the control tower be at the origin.
Assume north to be +y direction
              east to be +x direction
          upward to be +z direction
The aircraft is 10 km west(x = -10km) and 15 km north(y = +15km) and 4000m above the ground(z = +4000m = +4km).
So the coordinate of the aircraft is (-10,15,4).

Distance\ from\ control\ tower\ or\ origin =  \sqrt{(-10)^2+15^2+4^2}\ km \\distance= \sqrt{100+225+16}\ km \\distance = \sqrt{341}\ km \\ distance=\boxed{18.47\ km}
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