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
