Verifying a Right Triangle In Exercises 23, (a) find the length of each side of the right triang

step 1 Okay, so they give us the following picture. They give us a triangle, the following points. This

Verifying a Right Triangle In Exercises 23, (a) find the...

Key Concepts

Right Triangle

A right triangle is a type of triangle that includes one angle measuring exactly 90 degrees. This classification sets the stage for applying specific geometric properties such as the Pythagorean Theorem, making it crucial for problems involving side length determination and validation of triangle properties.

Pythagorean Theorem

The Pythagorean Theorem is a fundamental principle in Euclidean geometry that states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. This theorem is widely used for determining unknown side lengths and verifying that a triangle is indeed right-angled.

Transcript

00:01 Okay, so they give us the following picture.

00:06 They give us a triangle, the following points.

00:11 This is the point 1 -0.

00:13 This is the point -13 -0, and this is the point -13 -5.

00:24 They ask us to find the lengths of the sides of this triangle.

00:27 So let's just call those lengths a, b, and c.

00:33 So the first way to do this, i'm going to do this in two ways, but both essentially use the pythagorean theorem.

00:39 First way of doing this is to just figure out what a and b are and then use the pythagorean theorem to figure out c.

00:46 So let's do that.

00:47 The a, which is the length of this side, is just going to be equal.

00:53 Well, you start at 1 in the x axis, and you move, you don't move in the y axis, so you just move to 13, which means that the length over here is 12.

01:03 You had to take 12 steps in order to go from 1 to 1.

01:06 13 so a is going to be 12 and similarly b well you start at zero in the y -axis and you move up to five and x does not change so that does not matter which means that the length of b is 5 using the pythagorean theorem we know that a squared plus b squared is equal to c squared whenever you're dealing with the right triangle and we say that the hypotenuse the side opposite if the right angle is c.

01:39 So that tells us that 12 squared plus 5 squared is going to be c squared.

01:47 And that tells us that 144, which is 12 squared plus 25, which is 5 squared, is 5 squared, is going to be c squared.

01:57 So that tells us that 1099 is going to be c squared.

02:04 Or in other words, c is equal to the square root.

02:07 We take the square root of both sides in order to find c, the square root of 169, which is equal to 13.

02:17 So c, let's just, like, c is equal to, well, it's hard to write down here.

02:26 So i'll just write it here...

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