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The summit of a mountain, 2075 m above base camp, is measured on a map to be 4585 m horizontally from the camp in a direction 32.4° west of north. Choose the x axis east, y axis north, and z axis up. What are x, y, and z?

  • vectors -

    They are distances east, north, and up.

    Oh, you mean the (x,y,z) coordinates of the mountain summit?

    We know z = 2075. (letting the base camp be at (0,0,0))

    Now it's just a 2-d problem.

    x = 4585 cos 122.4 = -4478
    y = 4585 sin 122.4 = 3871

    (x,y,z) = (-4478,3871,2075)

    For extra points: how far is it directly from base camp to the summit?

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