how do you find the angle of a roof rise if it is built on a 1:4 slope

Question

How do you the roof rise angle on a shed built on a 1:4 slope.

Answer 1

tan(angel)=1/4=0.25

take the invers tangent(0.25)=14.03624347 deg

Comments

Slopes are normally quoted as a ratio 1:x where the slope distance is x. This is different from the horizontal distance. A 1:4 slope is therefore the sine rather than the tangent of the slope angle. But in practice the tangent of a gentle slope angle is approximately equal to the sine. The concept of slope in everyday use (surveying, for example) is different from the mathematical concept as used in graphs.

Answer 2

A 1:4 slope means for every measure of 4 along the slope there is a vertical drop of 1. This means that the angle of slope to the horizontal is opposite/adjacent=sine of the angle, x. If sin(x)=1/4, x=14.5 degrees approx.