Calculate the magnitude of the horizontal vector that is 100 units long and is oriented at 45 degrees

Your question is somewhat twisted up. We would be justified in simply asking you to correct the question. But I think I know what you're talking about, so I'll try to answer it.

A horizontal vector is one that's oriented at an angle of zero degrees, not 45 degrees. I think what you want is the horizontal component of the vector that you're describing.

Its horizontal component is 100 cos (45) = 100 / √2 = 70.71 units.