In my physics class we did a lab where we attached one end of a string to a .5 kg cart and the other end to a force meter which was all on a ramp. As we increased the angle of the ramp, the tension increased proportionally until the angle reached 45 degrees. From 45 degrees to 90 degrees, as we increased the angle, the tension approached m9.8. I understand why it approaches m9.8, but why does that start at 45 degrees?

The tension on the rope is equal to the mass of the cart times the sine of the angle of the ramp. For small angles the angle, in radians, is approximately equal to the sine of the angle. As the angle becomes larger the difference becomes larger and it begins to become significant around Pi/4 which is 45°. Try it with a calculator and you'll see what I mean. Set it to radians and enter small values and calculate the sine and you'll see that for small radians angle=sine(angle).