In this video you will learn…
· How to solve a word problem using the Pythagorean Theorem
· Simple rules for setting up Geometry word problems
· How to apply the Pythagorean theorem to find the hypotenuse of a right triangle
· If given two sides of a right triangle how to find the missing sideTranscript
Pythagorean Theorem examples
Today we are going to look at applying the Pythagorean Theorem. So here is our 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? I'm going to start with the rules of working with a word problems in Geometry. So here are the rules, the 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 we do know 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. So 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. So now we are going to apply the Pythagorean Theorem. A squared plus B squared plus C squared. So I will plug in 4 for B and 12 for C and I’m going to have to solve for A. 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. So 144 minus 16 is 128 is equal to A squared. To undo a square you take the square root so the square root of 128, so to find the square root of 128 I will make a factor tree. So 2 times 64 and 64 is a perfect square (square root of 64 is 8) so I take my pair out 8 square root 2 so that is how long A is. 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.
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