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dietrich_harmon
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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
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

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dietrich_harmon Group TitleBest ResponseYou've already chosen the best response.0
@Getmoney
 one year ago

robtobey Group TitleBest ResponseYou've already chosen the best response.0
My guess is\[\text{area}=2\left(\frac{w}{2}\text{Sec}\left[\text{ArcTan}\left[\frac{4}{12}\right]\right]L\right) \]
 one year ago

robtobey Group TitleBest ResponseYou've already chosen the best response.0
dw:1354215077572:dw
 one year ago

robtobey Group TitleBest ResponseYou've already chosen the best response.0
\[\text{edge}=\left(\frac{w}{2}\right)\text{Sec}[\theta ] \]where\[\theta =\text{ArcTan}\left[\frac{4}{12}\right] \]area of roof = \[2(\text{edge} * L) \]
 one year ago

dietrich_harmon Group TitleBest ResponseYou've already chosen the best response.0
so the answer is
 one year ago

robtobey Group TitleBest ResponseYou've already chosen the best response.0
\[2\left(\frac{w}{2}\text{Sec}\left[\text{ArcTan}\left[\frac{4}{12}\right]\right]L\right)=\frac{1}{3} \sqrt{10} L w \]
 one year ago
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