Find coordinates from the length of two lines

Question

A corner of the base of a building is 200 feet away from the surveyor, in a direction 40 degrees north of east, and the building is 150 feet high. What are the coordinates of the point at the top of the building directly above the corner?

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So 200 and 150 are two separate lengths of the triangle sides and we have a 40 degree angle given to work with.

I am having trouble understand how to find the coordinates of a point in the 3d plane described above and how to use the information given in the problem. Here is my crappy geometric intuition-drawing about it, but I think it is flawed.

Also by "coordinates", it wants a 3d vector $(x_1, x_2, x_3)$ right or am I understanding that wrong?

Edit:

So we are given $x_3 = 150$.

from pythag, we get $c = 250$. I guess we would also know that the top of the building, $x_1 = 200$. We also know the other angles are both $90^{\circ}$ and $180-90-40=50^{\circ}$. What trigonometry would I use to find $x_2$?

edit: updated drawing

Answer 1

Here is how the figure should be drawn. Those lines in red are on the ground.