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Advanced Math/Proving Pythagorus' theorum using trigonometry

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Expert: - 1/23/2012


Question
QUESTION: Hi Scott,
In my senior year at school, our maths teacher taught us how to prove Pythagorus' theorum using algebra, but as this was around 30 years ago, I have forgotten it all.
Can you please show me how it is done again?

Thanks.

ANSWER: Ways to prove it are found in http://www.mathsisfun.com/pythagoras.html

Open it up and page down to the title, "Another, Amazingly Simple, Proof".

If you want to use scissors, ruler, and a pencil, right above that is,
"And You Can Prove The Theorem Yourself!"

There is also, right below that last proof, a spot that can be clicked on called,
"proof by adding the areas".

If you want more ways to do it, down at the bottom of that window another window can be called up by clicking the underlined Phythagorean Theoren in the box with the, "here's more" out front.


---------- FOLLOW-UP ----------

QUESTION: Hi Scott,
Appologies, but I made a mistake in my question to you. What I actually want to know is how to prove Pytharorus' Theorum using Trigenometry.

Thanks.

Answer
It is known that sin²(x) + cos²(x) = 1.

It is also known that if the sides of a right triangle are of lenth a and length b,
and the hypotenuse is of length c, then sin(A) = a/c and cos(B) = b/c.

Putting this in the equation gives (a/c)² + (b/c)² = 1.
Multiplying by c² gives a² + b² = c².

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Scott A Wilson

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I can answer any question in general math, arithetic, discret math, algebra, box problems, geometry, filling a tank with water, trigonometry, pre-calculus, linear algebra, complex mathematics, probability, statistics, and most of anything else that relates to math. I can even tell you it takes me over 2,000 steps to go a mile, but is that relevant?

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Experience in the area; I have tutored people in the above areas of mathematics for almost two years in AllExperts.com. I have tutored people here and there in mathematics since before I received a BS degree almost 25 years ago. In just two more years, I received an MS degree as well, but more on that later. I tutored at OSU in the math center for all six years I was there. Most students offering assistance were juniors, seniors, or graduate students. I was allowed to tutor as a freshman. I tutored at Mathnasium for well over a year. I worked at The Boeing Company for over 5 years. I received an MS degreee in Mathematics from Oregon State Univeristy. The classes I took were over 100 hours of upper division credits in mathematical courses such as calculus, statistics, probabilty, linear algrebra, powers, linear regression, matrices, and more. I graduated with honors in both my BS and MS degrees. Past/Present Clients: College Students at Oregon State University, various math people since college, over 7,500 people on the PC from the US and rest the world.

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My master's paper was published in the OSU journal. The subject of it was Numerical Analysis used in shock waves and rarefaction fans. It dealt with discontinuities that arose over time. They were solved using the Leap Frog method. That method was used and improvements of it were shown. The improvements were by Enquist-Osher, Godunov, and Lax-Wendroff.

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Master of Science at OSU with high honors in mathematics. Bachelor of Science at OSU with high honors in mathematical sciences. This degree involved mathematics, statistics, and computer science. I also took sophmore level physics and chemistry while I was attending college. On the side I took raquetball, but that's still not relevant.

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I earned high honors in both my BS degree and MS degree from Oregon State. I was in near the top in most of my classes. In several classes in mathematics, I was first. In a class of over 100 students, I was always one of the first ones to complete the test. I graduated with well over 50 credits in upper division mathematics.

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My clients have been students at OSU, people nearby, friends with math questions, and several people every day on the PC, and you're probably make one more.

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