Question

A gutter at the edge of a roof drops 2 inches for every 30 feet of length. The measure of the angle to the nearest tenth of a degree that the gutter makes with the roof is ____ degrees.

Answer 1

About 0.3 degrees, by estimation.  
The sixty-to-one rule is useful here.  At a distance of 60 units, the angle in degrees and the distance (in units) are about equal for small angles.  
Thirty to two inches is the same as sixty to four inches, about a third of a foot, so the angle must be about a third of a degree.  Rounded it gives 0.3.  
My horribly antiquated TI-82 thinks the answer is about 0.3183 by this methodtan−1(1/180)≈0.3183