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dietrich_harmon

  • 3 years 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.

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  1. dietrich_harmon
    • 3 years ago
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  2. dietrich_harmon
    • 3 years ago
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    @Getmoney

  3. robtobey
    • 3 years ago
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    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
    • 3 years ago
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    |dw:1354215077572:dw|

  5. robtobey
    • 3 years ago
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    \[\text{edge}=\left(\frac{w}{2}\right)\text{Sec}[\theta ] \]where\[\theta =\text{ArcTan}\left[\frac{4}{12}\right] \]area of roof = \[2(\text{edge} * L) \]

  6. dietrich_harmon
    • 3 years ago
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    so the answer is

  7. robtobey
    • 3 years ago
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    \[2\left(\frac{w}{2}\text{Sec}\left[\text{ArcTan}\left[\frac{4}{12}\right]\right]L\right)=\frac{1}{3} \sqrt{10} L w \]

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