Question

A barn roof has a 35° rise, and the barn is 32 feet wide.a.How high does the roof rise?b. What length rafter is needed to have a 6 inch overhang?

Answer 1

a)

`\begin{gathered} \theta\text{ = 35} \\ \text{opposite = Height} \\ \text{Adjacent = 32} \\ \tan \theta\text{ = }\frac{opposite}{\text{adjacent}} \\ \tan 35\text{ = }(H)/(32) \\ 0.7\text{ = }(H)/(32) \\ H=32\text{ x 0.7} \\ H\text{ = }22.4\text{ f}eet \end{gathered}`

b)

Hypotanuse = length of rafter = x

`\begin{gathered} \cos \theta\text{ = }\frac{adjacent}{\text{hypotanuse}} \\ \cos \text{ 35 = }(32)/(x) \\ 0.819\text{ = }(32)/(x) \\ \text{Cross multiple} \\ 0.819x\text{ = 32} \\ \text{divide through by 0.819} \\ x\text{ = }(32)/(0.819) \\ x\text{ = 39.07 f}eet\text{ } \\ \\ \end{gathered}`