Building a Roof

We are building a roof. Our blueprints mandate that the pitch of the roof should be 11/18, but that's all the information we have. We've also been given a beam to function as the run of the roof, which measures 22 feet. We draw a sample triangle and label it "Triangle 1".
One builder suggested we use the tangent of our sample triangle to find the angle of elevation. Surprisingly, he brought his calculator to the work site, so we utilized its inverse tangent function to find the angle: 31.4 degrees. Figure 1 shows his notes.

Since Triangle 1 and Triangle 2 are similar (with 3 congruent angles), we can use a ratio between the adjacent and opposite sides of Triangle 1 and set it equal to the ratio between the respective sides of Triangle 2.
Now we can make the height of Triangle 2 our variable x, and solve to get 6.72 feet. {Figure 2}

To find the rafter line, all that's left to do is use the Pythagorean theorem and plug in our rise and run values, as shown in Figure 3.

Now with each value laid out, we can cut and begin to construct this roof.