Date: 3/30/96 at 12:19:29 From: Anonymous Subject: Right Triangles Is there an easy way to remember the different right triangles and how to find the lengths of missing sides? I already know that in any right triangle (a*a) + (b*b) = (c*c)
Date: 3/30/96 at 22:45:30 From: Doctor Jodi Subject: Re: Right Triangles Hi there! Well, there are a LOT of different right triangles. In fact, there are INFINITELY MANY right triangles. So, no, I don't think *anyone* could remember all of them. If you want to know more about Pythagorean triples, here's a cool trick I stole from http://www.maths.uts.edu.au/number/triples.html : ______ Here is an unusual way to find Pythagorean triples. Use some doodle paper to make your own example. Take any two fractions whose product is 2. | 3/2, 4/3 Add 2 to each number. | 7/2, 10/3 Cross multiply to get integers a, b in the same ratio. | 21, 20 Calculate a^2 + b^2. | 21^2+20^2 | = 441 + 400 = 841 Take the square root, and call it c. | sqrt(841) = 29 It always happens that c is an integer, so a, b, and c give a Pythagorean triple. (In the example here, we have found the Pythagorean triple 20, 21 and 29.) ______ If you already have two numbers of a Pythagorean triple and you want to find the other, you can use the Pythagorean formula (a^2 + b^2 = c^2). Any ideas on how you could figure out whether the 2 numbers you already have are the hypotenuse or one of the other sides? Write back if you have more questions! -Doctor Jodi, The Math Forum
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