vectors
posted by Millie on .
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?

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 2d 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?