Because that's the hypotenuse.

This is the hypotenuse.

So that right there is the hypotenuse.

The side that we call the hypotenuse.

The hypotenuse will always be the longest side.

Alright, a right triangle's hypotenuse has length 5.

So we need to figure out the hypotenuse here.

So the hypotenuse is now going to be five.

But notice, in this situation, 35 is a hypotenuse.

And that longer side is call the hypotenuse. And in all cases, the hypotenuse is the side opposite the 90 degree angle.

This or this squared, which is the height squared, is equal to your hypotenuse squared, this is your hypotenuse squared, minus the other side squared.

You only have a hypotenuse when you have a right triangle.

Well, c, in this case, once again, it is the hypotenuse.

He didn't call it the hypotenuse, he called it the shortcut distance.

(Video) Salman Khan So the hypotenuse is now going to be five.

And when I say the shorter side, I mean relative to the hypotenuse.

Let's say the hypotenuse is in green just so we get our color coding nice.

So what was the old route? Well the old route was the hypotenuse of this triangle, right?

The side opposite the right angle, or the 90 degrees, is a hypotenuse, or the longest side.

The sum of the squares of these two sides are going to be equal to 14 squared, the hypotenuse squared.

The distance between this point and 0 it's the hypotenuse of this right triangle. So we just use the Pythagorean theorem.

So we know that a squared plus 3 squared is equal to the hypotenuse squared, the side opposite the 90 degree angle.

Maybe the base of the triangle right over here is 4. and then the hypotenuse of the triangle over here is 5.

Let's call that f. f squared plus b squared is going to be equal to the hypotenuse squared, which in this case is d2 or a.

Let me write down the word logarithm just because it is another strange an unusual word, like hypotenuse , and it's good to at least see it once.

So we get w squared, this side squared. plus 7 squared, this other side squared, is going to be equal to the hypotenuse squared, square root of 74 squared.

And the Pythagorean Theorem tells us that the sum of the squares of the shorter side will be equal to the square of the hypotenuse, so the square of the longer side.

Pythagorean theorem, x squared plus 2 squared is equal to 5 squared because 5 is the hypotenuse. x squared plus 4 is equal to 25, subtract 4 from both sides. x squared is equal to 21.

And what the Pythagorean theorem tells us is that the sum of the squares of the shorter sides is going to be equal to the square of the longer side, or the square of the hypotenuse.

This long side, the side that is the longest side of our right triangle, the side that is opposite of our right angle, this right here it's c in this example this is called a hypotenuse.

So x squared plus 5 squared plus 25 is going to be equal to the hypotenuse squared, it's equal to 100. x squared is equal to 100 minus 25, 75. x is equal to the square root of 75.

And you can verify that this right triangle the sides work out we know from the Pythagorean theorem, that 3 squared plus 4 squared, has got to be equal to the length of the longest side, the length of the hypotenuse squared is equal to 5 squared so you can verify that this works out that this satisfies the Pythagorean theorem.

So what we have right over here, we have two right angles, this is the right angle here, this one clearly has to be, the way we constructed it, it's, it's at a right angle, and then we know that, we know that CM is going to be equal to, we know that CM is going to be equal to, is going to be equal to itself, and so we know by, this is a right angle, we have a leg and we have a hypotenuse, we know by the RSH postulate,