Why Does Subtracting a Vector's Angle from 90 Degrees Determine Its Complement?

[Bashyboy]

In the example problem--which is dealing with vectors--an airplane is seen 215 km from an airport, making a 22 deg angle with respect to the y-axis. What the author does is simply subtract 22 deg from 90, to find the angle it makes with the x-axis. Why is the author allowed to do this? Does this have something to do with complementary angles? Could someone please explain this to me? Thank you.

 

[conquest]

the x and y angles supposably are orthogonal. (as they are in the cartesian coordinate system with the standard inner product). So the answer is yes he can just do this if you want a more elaborate way of calculating that this is true do the following:

draw the quarter unit circle form the x to y axes. Then the line with an angle of 22 degrees w.r.t. the y-axis. it intersects the circle at the coordinate:
(sin x, cos x) where the argument of cos and sin is in degrees for convenience now.
now find x.

You know that if you flip around the axis i.e. you switch x and y you end up in the point (cos 22, sin 22) so we solve sin x = cos 22 and cos x = sin 22. thus x = 90 - 22 degrees.

Again this really isn't needed