The first thing to do is to determine the angles that the Hip/Valley rafter makes with the 90° corner. These angles are important because they are also the cheek cut angles for the Hip/Valley rafter and the side cut angles for the Hip/Valley Jack rafters.

One way of determining them is as follows; take the different roof rises, 7 and 12 and divide the smaller by the larger (see you can do it the other way also, but I like to do it like that). Take the answer and perform the Arc Tangent function to it. This function is the noted on many calculators as tan^-1.

7/12 = .5833

tan^-1(.5833) = 30.25°

This is the angle of the cheek on the 7/12 of the Hip/Valley rafter and the Jack rafter cut on the 12/12 side. Finding the complement of this angle will produce the angle for the cheek cut on the 12/12 side and the Jack rafter cut on the 7/12 side.

30.25° - 90.00° = 59.74°

This is the for the cheek cut on the 12/12 side of the Hip/Valley rafter and the Jack side cut for the 7/12 side Jack rafters. It’s important to note that it doesn’t matter which pitch you divide into, the answers will still be the same. Let’s look at it the other way now.

12/7 = 1.7142

tan^-1(1.7142) = 59.74°

So whether you divide the smaller by the larger or vice versa, you will still get the same answers. The graphic below illustrates this and also shows the relationship between the sides and unit run of the Hip/Valley rafter.