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An air-traffic controller observes two aircraft on his radar screen. The first is at altitude 850 m, horizontal distance 20.0 km, and 24.5° south of west. The second aircraft is at altitude 1100 m, horizontal distance 18.0 km, and 16.0° south of west. What is the distance between the two aircraft? (Place the x axis west, the y axis south, and the z axis vertical.)

  • science -

    i do not know if this is process you'll be fine. after finding the spatial coordinates of tha sobstitute in the distans equation between two points:

    first aircraft angle a1=24.5*2Pg/360=0.43Rad
    second aircraft angle

    first aircraft d1=20000m
    x1=d1*sen(a1) y1=d1*cos(a1) z1=850m

    second aircraft d2=18000m
    x2=d2*sen(a2) y2=d2*cos(a2) z2=1100m


  • science -

    using x,y,z as coordinates, in km,
    p1 = (20cos24.5,20sin24.5,0.85)
    = (18.199,8.294,0.85)

    p2 = (18cos16,18sin16,1.1)
    = (-17.303,-4.961,1.1)

    d^2 = (18.199-17.303)^2 + (8.294-4.961)^2 + (.85-1.1)^2
    d = 3.460km

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