## dietrich_harmon Group Title A carpenter is building a roof on a barn that is w feet wide and ℓ feet long. The roof will be covered by corrugated tin and the carpenter needs to know the area of the roof to estimate the amount of tin to purchase. The roof will have a pitch of 4:12. Find an expression for the area of the roof in terms of w and ℓ feet long. Note: the pitch of a roof is ratio of the rise to the run as in the picture below. one year ago one year ago

1. dietrich_harmon Group Title

2. dietrich_harmon Group Title

@Getmoney

3. robtobey Group Title

My guess is$\text{area}=2\left(\frac{w}{2}\text{Sec}\left[\text{ArcTan}\left[\frac{4}{12}\right]\right]L\right)$

4. robtobey Group Title

|dw:1354215077572:dw|

5. robtobey Group Title

$\text{edge}=\left(\frac{w}{2}\right)\text{Sec}[\theta ]$where$\theta =\text{ArcTan}\left[\frac{4}{12}\right]$area of roof = $2(\text{edge} * L)$

6. dietrich_harmon Group Title

$2\left(\frac{w}{2}\text{Sec}\left[\text{ArcTan}\left[\frac{4}{12}\right]\right]L\right)=\frac{1}{3} \sqrt{10} L w$