Pythagorean Theorem
"a² + b² = c²"
The Pythagorean theorem provides a formula to calculate the third side of a triangle when given the other two sides. The formula can be used for any side of any right triangle. The song also introduces students to terms like legs and hypotenuse. This video puts the Pythagorean theorem in real-world terms, helping students visualize examples in which the formula comes into play.
“Uncle Ricky?”
Yes, youngins?
“Would you tell us that story about Pythagoras?”
Ah, and the Pythagorean Theorem?
“Yeah!”
Ok, gather round.
“Ok.”
Let’s go.
Let me tell you 'bout a man named Pythagoras,
He was a mathematician, but way past the average.
Everywhere you go, you can hear people cheer him,
'Cause everybody's using the Pythagorean Theorem.
How do you do it? Well it's not hard,
All you need is a right triangle to start.
Yeah, the two short sides are legs,
The long side has a different name instead:
The hypotenuse, and in case you get tangled,
It's the side that's always across from the right angle.
So you got three sides, but you only know two,
This is where Pythagoras knew what to do.
He named the two short sides a and b,
And he called the hypotenuse c.
Then he fit all of it into an equation,
And it became the theorem that's sweeping the nation!
We're doing the Pythagorean Theorem, haven't you heard?
When you know 2 sides, you can find a 3rd.
a2 + b2 = c2
Solve for any one, then you're almost done.
'Cause when you get your answer, you're still not through,
Don't forget that you've gotta solve for the square root!
True, now check out this day in the life of Pythagoras and see how he used math.
Pythagoras was playing baseball with his peeps,
At second base and his throw had reach.
You see he knew that he was 90 ft from first base,
But he wanted to see how far he was from home plate.
From home to first was another 90 ft,
So it looked like his equation was complete.
902 + 902 = c2
Take the square root of c2 then we're home free, yeah.
When the game was done, Pythagoras took a walk,
And he saw a building on fire, right down the block.
The people inside were trapped 40 ft up,
The fire truck was 30 ft away and it was stuck.
Time to find the hypotenuse, there it is!
And the Pythagorean Theorem's what we've got to use,
302 + 402 = c2
Solve for c, that's the size of the ladder that we need, right?
"Yeah, it was crazy Pythagoras went from playing baseball to saving people from a burning building and the whole time he used math. That’s why..."
We're doing the Pythagorean Theorem, haven't you heard?
When you know 2 sides, you can find a 3rd.
a2 + b2 = c2
Solve for any one, then you're almost done.
'Cause when you get your answer, you're still not through,
Don't forget that you've gotta solve for the square root!
True, and don't forget those Pythagorean triples if you want to be a real whiz. You know:
3, 4 and 5.
5, 12 and 13.
And 7, 24 and 25.
They even work in multiples, too. That’s how you do the Pythagorean Theorem in style. You dig?
Pythagoras was a Greek mathematician, born 570 BCE. He lived a very long time ago, but we still talk about him today because he discovered a theorem that has been used ever since when dealing with right triangles.
Pythagoras was a Greek mathematician, born 570 BCE. He lived a very long time ago, but we still talk about him today because he discovered a theorem that has been used ever since when dealing with right triangles.
A right triangle is a triangle that includes one right angle, measuring 90 degrees. It doesn’t matter which of the three angles is 90 degrees--as long as one of them is, it’s a right triangle.
A right triangle is a triangle that includes one right angle, measuring 90 degrees. It doesn’t matter which of the three angles is 90 degrees--as long as one of them is, it’s a right triangle.
The long side of a right triangle is called the hypotenuse. The hypotenuse is always opposite the right angle of the triangle. The two shorter sides are called legs. Though other triangles can have a longest side, it is only called the hypotenuse in a right triangle.
The long side of a right triangle is called the hypotenuse. The hypotenuse is always opposite the right angle of the triangle. The two shorter sides are called legs. Though other triangles can have a longest side, it is only called the hypotenuse in a right triangle.
When it comes to using the formula for the Pythagorean theorem, you use letters for each side. The legs are called a and b--it doesn’t matter which of the two is used for which leg. The hypotenuse is always called c. This helps you keep track of which side is which when you use the formula.
When it comes to using the formula for the Pythagorean theorem, you use letters for each side. The legs are called a and b--it doesn’t matter which of the two is used for which leg. The hypotenuse is always called c. This helps you keep track of which side is which when you use the formula.
The Pythagorean theorem states that the sum of the squares of the two legs of a triangle is equal to the square of the hypotenuse. This is true for every right triangle. If given two sides of any right triangle, you can use this formula to find the length of the third side.
The Pythagorean theorem states that the sum of the squares of the two legs of a triangle is equal to the square of the hypotenuse. This is true for every right triangle. If given two sides of any right triangle, you can use this formula to find the length of the third side.
It’s easy to forget that you’re dealing with the squares of each side, not the lengths of the sides themselves. Remember to solve for the square root--that will be the value of the side you’re looking for.
It’s easy to forget that you’re dealing with the squares of each side, not the lengths of the sides themselves. Remember to solve for the square root--that will be the value of the side you’re looking for.
Good ol' Pythagoras was a regular Babe Ruth of his era. Or we're sure he would have been if baseball had been invented.
Good ol' Pythagoras was a regular Babe Ruth of his era. Or we're sure he would have been if baseball had been invented.
How far is it from 2nd base to home? Let's use the theorem.
The two legs are both 90 ft. That gives us this equation: 902 + 902 = c2 All you have to do is solve for c.
8100 + 8100 = c2
c = √16200 = 127.3 ft
How far is it from 2nd base to home? Let's use the theorem.
The two legs are both 90 ft. That gives us this equation: 902 + 902 = c2 All you have to do is solve for c.
8100 + 8100 = c2
c = √16200 = 127.3 ft
If the people are 40 feet high in the building and the fire truck is 30 feet away, how long does the ladder from the truck to the building have to be? The two given sides are the legs, which means you have to solve for the hypotenuse.
c2 = 1600 + 900 = 2500
That means c = 50 ft.
If the people are 40 feet high in the building and the fire truck is 30 feet away, how long does the ladder from the truck to the building have to be? The two given sides are the legs, which means you have to solve for the hypotenuse.
c2 = 1600 + 900 = 2500
That means c = 50 ft.
Pythagorean triples are sets of three whole numbers that satisfy the Pythagorean theorem. 3, 4, and 5 is the most basic Pythagorean triple.
32 + 42 = 52
Since 9 + 16 = 25
Multiples of a Pythagorean triple also work. Take the doubles of the previous example, 6, 8, and 10. Some other Pythagorean triples are:
8, 15, 17;
9, 40, 41;
11, 60, 61;
and 12, 35, 37.
Pythagorean triples are sets of three whole numbers that satisfy the Pythagorean theorem. 3, 4, and 5 is the most basic Pythagorean triple.
32 + 42 = 52
Since 9 + 16 = 25
Multiples of a Pythagorean triple also work. Take the doubles of the previous example, 6, 8, and 10. Some other Pythagorean triples are:
8, 15, 17;
9, 40, 41;
11, 60, 61;
and 12, 35, 37.
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