this is a mathematical investigation and i would like to know. if all the 3 sides are given even the hypotenuse how exactly do i prove that the angle C^ / the hypotenuse is 90 degrees?
Answers (1)
According to Pythagorean theorem, for any right triangle with sides a and b and hypotenuse h, the square of the hypotenuse is equal to the sum of the squares of the other two sides. The hypotenuse must be the longest side, so AB must be the hypotenuse. Then, AB^2 + CA^2 = AB^2.
But, since the length can be simplified to the shortest, we just simply look at the simplified length. That is, AB=3, CA=4, and AB=5. 3, 4, and 5 are the order of right angle sides, just like 6, 8, and 10. So, 4.5 , 6, and 7.5 must be the order of right angle sides too.
It's proved.