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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
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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robtobeyBest 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

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

robtobeyBest 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_harmonBest ResponseYou've already chosen the best response.0
so the answer is
 one year ago

robtobeyBest 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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