Describe and correct the error in using the Pythagorean...

Describe and correct the error in using the Pythagorean Theorem
$c^{2} \square a^{2}+b^{2}$
$x^{2} \square 10^{2}+26^{2}$
$x^{2} \square 100+676$
$x^{2} \square 776$
$x \square \sqrt{776}$
$x \approx 27.9$

Key Concepts

Pythagorean Theorem

The Pythagorean Theorem asserts that in a right triangle the square of the hypotenuse (the side opposite the right angle) equals the sum of the squares of the other two sides. This relation is valid only when the correct sides are identified and substituted into the formula.

Identification of the Hypotenuse

A key step in correctly applying the theorem is ensuring that the hypotenuse—the longest side of the right triangle—is properly identified. Misidentifying which side is the hypotenuse can lead to plugging the wrong values into the formula. In the error shown, the unknown side was taken as the hypotenuse even though the given side lengths indicated that a different side should be used as the hypotenuse. Correcting this mistake involves determining which side of the triangle is longest, then setting up the equation so that the square of that longest side is equated to the sum of the squares of the other two sides.

Transcript

00:01 So for this problem, we are asked to solve for x and describe how the book has been an error in solving for x.

00:11 Now, one thing i find useful is to see how we can solve for x correctly so that we can compare a correct answer with a wrong answer, and that makes it easier to find the error.

00:22 So here, we have a right triangle because we have a right angle in three sides.

00:30 And as to the shape, so it's a right triangle.

00:34 So in order to solve for x, which is the length of one of the legs of the right triangle, we will have to use pythagrin theorem.

00:43 So let's make sure we set up pythagorean theorem correctly by finding which side of the right triangle is the hypotenuse.

00:51 Well, the hypotenuse is the side of the right triangle that's opposite to that of the right angle.

00:57 So i like drawing these little arrows to show me where the opposite sign of the right angle is.

01:04 So you can see that the hypotenuse has a length of 26.

01:08 So when we set up pythagrin theorem equation, we get x squared plus 10 squared is equal to 26 squared.

01:19 Okay, so far still good.

01:21 So let's attract 10 square from the outside.

01:23 So x squared is equal to 26 squared minus 10 squared.

01:26 X squared is equal to 6776 minus 10 squared which is 100 so that x squared is equal to 576 we can take the square root both sides we don't need a plus minus because having minus signs means that we have x be a negative length actually be a negative value and the length of the like would be negative which doesn't make sense so we only need to take the positive of this route and we get x is equal to 24.

02:01 Okay, so let's compare with the book's way and it's compared to our...

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