Inverse Tangent

When both legs are known, the tangent links them and arctan gives the angle. This is how a slope becomes an angle. A road that climbs 1 m for every 10 m along the flat has tan(theta) = 1/10, so theta = atan(1/10), about 5.71°.

Road signs give that slope as a percentage: 10% means 10 m up for 100 m along, the same 1/10. A 10% hill sounds steep, yet its angle is under 6°. A slope of 100% is a rise equal to the run, an angle of 45°.