A house attic as shown has a roofline with a slope of 5up

Chapter 3, Problem 3.2.18

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A house attic as shown has a roofline with a slope of 5up for every 12of horizontal run; this is a slope of 512. Since the roofline starts at 4above the floor, it is not possible to stand in much of the attic space. The owner wants to add a dormer with a 212 slope, starting at a 7height, to increase the usable space. a. With height and floor distance coordinates as shown on the house sketch, find a formula for the original roofline, using R for roof height and F for floor distance from the wall. Also find a formula for the dormer roofline, using D for dormer roof height and F for floor distance from the wall. b. Make a graph showing the R and D roof height lines for floor distances F from 0to 18. c. At what height and floor distance will the dormer roofline intersect the existing roofline? d. How far do you need to measure along the horizontal floor distance to give 66of head room in the original roofline? What percent of the horizontal floor distance of 18 ft allows less than 66of head room?