What is the Pythagorean Theorem?
The Pythagorean Theorem. The Pythagorean Theorem states that the sum of the squares of the legs of a right triangle is equal to the square of the hypotenuse of a right triangle. The legs of a right triangle are the two sides that form the right angle.
The hypotenuse is the side that’s across from the right angle. Let’s look at two examples. Find the missing sides of the right triangles. On this first example, we’re given the lengths of the two legs of the right triangle, and what we need to find is our hypotenuse.
The hypotenuse again is the C in the Pythagorean Theorem. What we’re trying to find is C. We’ll start by writing the Pythagorean Theorem. A squared plus B squared is equal to C squared. A can be either one of the legs and B can also be either one of the legs.
4 squared plus 3 squared is equal to, (the hypotenuse is what we don’t know), so we’ll leave it as C our variable that we’re trying to find. Then we simplify. 4 squared is 16, plus 3 squared is 9, is equal to C squared. Then we need to combine like terms.
16 plus 9 is 25. 25 is equal to C squared. We’re almost there, but we haven’t found C yet. Right now we know what C squared equals, and that’s 25. But, to find C we need to do the opposite of squaring which is square rooting. We square root both of our sides.
The square root of 25 is 5, and the square root of C squared is C. Which means that our hypotenuse is 5. On this next triangle, we know the hypotenuse this time, across from the right angle is our hypotenuse, and that’s given to us as 17. What we’re trying to find now is one of our legs.
This leg can either be your A or your B. I’m going to call it my B. Again, we’ll start with Pythagorean Theorem; A squared plus B squared is equal to C squared. A and B are your legs and C is your hypotenuse.
We know one of our legs 15 so i’ll substitute that for A squared plus, we’re trying to find our other leg, B squared we don’t know it, equals, and then our hypotenuse which is our C, is 17 so 17 squared. Now, we need to simplify. 15 squared is 225 plus B squared is equal to 17 squared is 289.
Since we’re trying to solve for B, that means we need to get B alone. To do that we’re going to have to subtract 225 from both sides. 225 minus 225 is 0. On the left side we’re left with B squared is equal to and then 289 minus 225. 9 minus 5 is 4, 8 minus 2 is 6, and 2 minus 2 is 0.
Again we found B squared, but we haven’t found B yet. To solve for B we need to take the square root of both sides. The square root of B squared is B and this squared is 64 is 8. That means that our other leg on our right triangle is 8.