Question

1. A barn roof has a 40° rise, and the barn is48 feet wide.a. How many feet does the roof rise?b. What length rafter is needed to have an8-inch overhang?

Answer 1

a) 40.27 approximately 40 ft

b) 40.94 approximately 41 ft

1) Let's sketch that to better grasp it

a. Let's use a trigonometric ratio for that rise of the roof since there's an angle of elevation. We'll use a tangent

`\begin{gathered} \tan (40)=(h)/(48) \\ h=48*\tan (40) \\ h\approx40.27\approx40\text{ ft} \end{gathered}`

b). Since we want to know how can we have an 8" inch overhang, let's firstly convert that to feet:

1 ft ----------12 "

y ---------- 8"

y=8/12

y=2/3 ft = 8"

So let's find out the length of this rafter, assuming this rafter will be placed like this

`\begin{gathered} h_{\text{rafter}}=40.276\text{ +0.666} \\ h_(rafter)=40.94\text{ ft} \end{gathered}`