Wednesday, March 4, 2009

Pythagorean Theorem


The Pythagorean Theorem is used to find a missing side length of a right triangle. It only works for right triangles (one with a right angle).

The formula to use is a2 + b2 = c2. A really good explanation of the formula and its derivation can be found here.

In order to use the theorem, you must know the parts of the triangle. Parts a and b of the theorem are the legs of the triangle. These are the side lengths that make up the right angle. The third side (longest side) is noted as c in the theorem.

Now substitute the values given into the theorem (formula) and solve the equation.

Example: A triangle has a side length of 6 cm and a side length of 8 cm. What is the length of the hypotenuse?

62 + 82 = c2
36 + 64 = c2
100 = c2
√100 = √c2
10 = c


Example: A triangle has a side length of 6 cm and a hypotenuse length of 12 cm. What is the length of the missing side?

a2 + 62 = 122
a2 + 36 = 144
a2 + 36 – 36 = 144 – 36
a2 = 108
√a2 = √108
a = √108
a = 6√3

Picture of triangle above from http://en.wikibooks.org/wiki/File:Right_triangle_shows_hyp_legs.PNG

2 comments:

D Johnson said...

i never quite new how to do this and i still dont its kinda hard.

http://www.ehow.com/members/stevemar2-articles.html said...

I like your blog. I also have a blog that is math-oriented. You can check it out at http://mathvariety.blogspot.com if you want.