Let's illustrate the given information.
To determine the angle of this rafter, we can use the tangent function. The formula is:
[tex]\tan \theta=\frac{opposite\text{ side}}{\text{adjacent side}}[/tex]Our angle in the illustration is the one colored in red. The opposite side of the angle measures 5.5 inches while the adjacent side measures 12 inches. Let's plug in this data to the formula above.
[tex]\tan \theta=\frac{5.5}{12}[/tex]To be able to get the measure of angle, let's get the arc tan of the angle.
[tex]\theta=\tan ^{-1}\frac{5.5}{12}\approx24.62[/tex]Hence, the rafter must be angled 24.62 degrees away from the ceiling joist of the house.
