A gable roof is to be constructed with a slope
of 28 degrees and a run of 27 ft 6 in. Calculate 
the rise of the roof. Express the answer in feet 
and inches to the nearest inch.

Here is a picture of the gable:



We'll cut off the triangle on the right, 
write 27 ft 6 in as 27.5 ft, and let x 
be the rise.



Now we see that since this is a right triangle,

                  side opposite 28°
tangent of 28° = ———————————————————
                  side adjacent 28°

              x
tan(28°) = ———————
            27.5

Put the tangent over 1:

 tan(28°)       x
—————————— = ———————
    1         27.5

Cross multiply:

x = (27.5)tan(28°)

x = 14.62200937 ft. 

To get that to the nearest inch,
we multiply the decimal part
.62200937 by 12 to get 7.464112448
inches which rounds to 7 inches.

So the rise is 14 ft 7 inches, to
the nearest inch.

Edwin