Math CentralQuandaries & Queries


Subject: Right triangle
Name: Rob
Who are you: Other

I am trying to determine how much to add for roof pitch. I guess the best way would be to use a right triangle as an example.

The base of the triangle is always 12 inches. The leg pointing straight up is a variable. I will say 6" in this example. By changing the variable how can i determine how much longer the hypotenuse than the base expressed in percent or decimal.
Thank you

Hi Rob.

Pythagorus' theorem tells us that in a right triangle, the side lengths are related by c2 = a2 + b2 where c is the hypotenuse.

So if "a" is the base (12 inches),
c2 = 144 + b2
c = sqrt(144 + b2)
c/0.12 = sqrt(144 + b2)/0.12

This form gives you the percentage size of the hypotenuse compared to the 12 inch base. For example, if you measure 6" for the height variable b, then

sqrt(144 + 62)/0.12 = 111.8 percent, so the hypotenuse is 111.8% of the base and hence you have to add 11.8% of the base measurement.

If it is steeper, you should get a higher percentage. For example, if you measure the height as 8", you get:

sqrt(144 + 8^2)/0.12 = 120.2 percent

Hope this is useful to you.
Stephen La Rocque.

About Math Central


Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.
Quandaries & Queries page Home page University of Regina PIMS