Solution:
c² = a² + b² = (7½)² + 6² (a:12::5:8,
whence a = 7½)
c = 9.60'
Expressing this run of valley in terms of 12" of run of common rafter
over b.
9.60':6'::x:12".
x = 19.20". (Check this value by scale drawing.)
Length of valley rafter, then, is found by taking 19.20" on the tongue with 10" (5/6 of 12") on the blade, advancing the setting as many times as there are feet in the run of the common rafter over b.
Fig. 88-a. Uneven Pitches
The numbers just given will give the plumb cut and the seat cut of this valley rafter.
(2) Find the side cut of the valley rafter when it rests against the ridge of the minor roof.
Solution: The side cut of the valley when allowed to rest in the plane of the
plate = angle B, [Fig. 88-a], whose tangent =
b/a = 6/7½ (= 12/15 = .800 = 38° 40')
Therefore, take 7½" on the blade (always the run of intercepted common rafter of major roof), and 6" on the tongue (always the run of the common rafter of the minor roof); scribe on the blade.
For side cut of valley rafter when it is to be fitted to a ridge of the major roof, the lay-out when in the plane of the plate is obtained by means of these same numbers, but the scribing is done on the tongue. This lay-out in either case is for the rafter when lying in the plane of the plate. Having secured this, proceed as in [Sec. 35], (2).
Side cuts of jacks for the minor roof are determined by the length of the ridge over a, [Fig. 88-a], and the length of the rafter over b. But the length of the ridge over a= the run of the intercepted common rafter of the major roof, 7%' here. A general rule may be derived, therefore: For the side cut of a jack on a minor roof take on the blade of the square the run of the intercepted common rafter of the major roof (inches for feet), and on the tongue take the length of rafter of the minor roof; scribe on the tongue, [Fig. 88-b]. For the side cut of jacks on a major roof, take on the tongue of the square the run of the common rafter of the minor roof, and on the blade the length of the intercepted common rafter of the major roof; scribe on the blade, [Fig. 88-c].