Working on a trig problem.

I am working on extremely skinny triangles for astronomy work, so if you imagine a right triangle where the vertical is short and the horizontal is VERY long, I want to find the ratio between the short side to long side, I figured out if I subtract the upper very small angle from 90 degrees and divide that by 1 radian, like 57.xxx/tiny angle in decimal degrees, I get the ratio directly. Anyone know why that is?
In the case I am pursuing, the ratio is 117,000 to 1, so its the decimal of 1 radian, 57.xxx/4.8E-4= 117.000 and change, just the number I need, but I don't understand why it does that. Anyone help?

Originally posted by sonhouse
I am working on extremely skinny triangles for astronomy work, so if you imagine a right triangle where the vertical is short and the horizontal is VERY long, I want to find the ratio between the short side to long side, I figured out if I subtract the upper very small angle from 90 degrees and divide that by 1 radian, like 57.xxx/tiny angle in decimal degr ...[text shortened]... 7.000 and change, just the number I need, but I don't understand why it does that. Anyone help?

for x close to 0, tan(x) is approximately x (when x is in radians).