How to Use the Pythagorean Theorem to Solve Word Problems.

Apply the Pythagorean Theorem
Today we are going to look at applying the Pythagorean Theorem.
Example problem. A 12 foot ladder is placed four feet from the base of a wall,
how far up the wall will the ladder reach?

Rules of working with a word problems in Geometry.
First rule is that you always draw a picture.
Get out your marker and draw a scenario of what this situation looks like.
Then I want you to label it.
Take all the information and label the picture, and since this is the Pythagorean Theorem.

We will identify where is A where is B and where is C and then we will plug everything into the Pythagorean Theorem, and solve for the unknown.

So let's go through the steps.

Let's draw a picture. We have a wall and we have a ladder leaning against the wall. (Draws this) and now let's label what we know.

We know this is a 12 foot ladder, and it is placed four feet from the base of the wall.

That means my four feet is here. (points to bottom of triangle) and I have the right angle here.

Now opposite the right angle is the hypotenuse or C that means the floor is B so A is missing.

I have now identified A, B, and C.

Apply the Pythagorean Theorem.

So let's square these out, four squared is 16, and 12 squared is 144 ,and I don't know my A squared.

Now, let's subtract 16 from both sides.
To undo a square you take the square root so the square root of 128, so to find the square root of 128

Make a factor tree.
A = 8 is how far up the ladder will reach.

You could also get the decimal version by originally taking the square root of 128 on your calculator, but the exact answer is 8 square 2. Hope this was helpful.