SOLUTION: A carpenter wants to construct a simple cabin with a pitched roof. The inside height of this “A-frame” cabin next to the wall must be 8 feet high. The owner wants the inside h

Algebra ->  Triangles -> SOLUTION: A carpenter wants to construct a simple cabin with a pitched roof. The inside height of this “A-frame” cabin next to the wall must be 8 feet high. The owner wants the inside h      Log On


   

Question 1012352: A carpenter wants to construct a simple cabin with a pitched roof. The inside height of this “A-frame” cabin next to the wall must be 8 feet high. The owner wants the inside height of the roof in the middle of the room (at the tallest point) to be 12 feet high. The owner wants the slope of the roof to be 1/3. How wide then must the cabin be?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Put this on a graph with the 8' wall on
the y-axis.
( 0,8 ) is the inside height of short wall
( x[1], 12 ) is the middle of the inside roof
( 2x[1], y[1] ) is the inside height of highest wall
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Equation for the ceiling line would be:
+y+=+m%2Ax+%2B+b+
+b+=+8+ ( y-intercept )
+m+=+1%2F3+ ( slope )
+y+=+%281%2F3%29%2Ax+%2B+8+
------------------
Plug in ( x[1], 12 )
+y+=+%281%2F3%29%2Ax+%2B+8+
+12+=+%281%2F3%29%2Ax%5B1%5D+%2B+8+
+12+-+8+=+%281%2F3%29%2Ax%5B1%5D+
+%281%2F3%29%2Ax%5B1%5D+=+4+
+x%5B1%5D+=+12+
--------------
Plug in
( 2x[1], y[1] )
+y+=+%281%2F3%29%2Ax+%2B+8+
+y%5B1%5D+=+%281%2F3%29%2A2x%5B1%5D+%2B+8+
+y%5B1%5D+=+%281%2F3%29%2A2%2A12+%2B+8+
+y%5B1%5D+=+8+%2B+8+
+y%5B1%5D+=+16+ ( this was an extra step )
-------------
+2x%5B1%5D+=+24+
The width of the cabin is 24'
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Here's a plot of this ceiling line:
+graph%28+700%2C500%2C+-4%2C+28%2C+-4%2C+20%2C+%281%2F3%29%2Ax+%2B+8+%29+