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| Math Central | Quandaries & Queries |
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Subject: Right triangle 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. |
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.
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