Question

What is the Pythagorean Theorem explain and use examples

Answer 1

So I typed this long response with pictures and OpenStudy freaked out because I tried to move the draw box thing. Stupid. But I screenshotted the answer. I'll draw back the pictures.



So the general equation is \[a^{2} + b^{2} = c^{2}\] .
And we can plug in the values from the picture to get: \[3^{2} + 4^{2} = 5^{2}\]
Solving that out, we have 9 + 16 = 25 and that's a true statement! Magical :)

So say we have this info now: We can solve for this just the same to get \[a^{2} + 4^{2} = 6^{2}\] with a being the term we don't know. So, \[a^{2}\] + 16 = 36. Rearranging, we have \[a^{2} = 20\] and then take the square root of both sides to get a = + \[\sqrt{20}\]. We only take the positive square root because we're talking about lengths, and lengths can't be negative here.