Usually the letters a, b, and c are used; in this case, a and b are adjacent to the right angle, and c is opposite to the right angle.
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Yes. If you square each of his legs and add them, the sum is equal to the square of his hypotenuse.
It does not.If you consider a right angled triangle with minor sides of length 1 unit each, then the Pythagorean theorem shows the third side (the hypotenuse) is sqrt(2) units in length. So the theorem proves that a side of such a length does exist. However, it does not prove that the answer is irrational. The same applies for some other irrational numbers.
You must find the x and y components of each vector. Then you add up the like x components and the like y components. Using your total x component and total y component you may then apply the pythagorean theorem.
6, 8, and 10 is simply a scaled up version of a 3,4,5 triangle (simply double each side). Since 3,4,5 is a Pythagorean triple, so is the scaled up triangle. Alternatively, since 6, 8, and 10 are integers (whole numbers) that fulfill the Pythagorean theorem (62 + 82 = 102 ), they are a Pythagorean triple.
Each side of the square is 20 inches and by using Pythagoras' theorem its diagonal is 20 times the square root of 2 which is about 28.284 inches rounded to 3 decimal places.