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### Course: 8th grade (Eureka Math/EngageNY) > Unit 3

Lesson 3: Topic C: The Pythagorean theorem- Intro to the Pythagorean theorem
- Pythagorean theorem example
- Pythagorean theorem word problem: carpet
- Pythagorean theorem intro problems
- Use Pythagorean theorem to find right triangle side lengths
- Pythagorean theorem with isosceles triangle
- Use Pythagorean theorem to find isosceles triangle side lengths
- Right triangle side lengths
- Use area of squares to visualize Pythagorean theorem
- Pythagorean theorem word problem: fishing boat
- Pythagorean theorem word problems
- Thiago asks: How much time does a goalkeeper have to react to a penalty kick?
- Garfield's proof of the Pythagorean theorem
- Bhaskara's proof of the Pythagorean theorem
- Pythagorean theorem proof using similarity
- Another Pythagorean theorem proof

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# Pythagorean theorem intro problems

Practice using the Pythagorean theorem to solve for missing side lengths on right triangles. Each question is slightly more challenging than the previous.

## Pythagorean theorem

The equation for the Pythagorean theorem is

where $a$ and $b$ are the lengths of the two legs of the triangle, and $c$ is the length of the hypotenuse.

*Want to learn more about the Pythagorean theorem? Check out this video.*

## Want to join the conversation?

- Is there any way on how to do Pythagorean theorem easier im having trouble understanding(52 votes)
- You can remember easy "Pythagorean Triples" like the famous 3-4-5 combo, with 5 being the hypotenuse. There are also some other not-as-famous triples like the 5-12-13 triple, the 7-24-25 triple, and the 9-40-41. Note that the hypotenuse of these "triples" is always the largest number.(26 votes)

- there is so much history in the comments(44 votes)
- i wonder how we figured out the pythagoream theorem(30 votes)
- It was proven by Pythagoras. There are several popular proofs (even one done by a former US president [Garfield]). Look up proof of Pythagoras Theorem on YouTube.(13 votes)

- when am I going to use this in life?(26 votes)
- Why do people always ask obvious questions and then get a ton of votes?!(26 votes)
- because it is easier to full around(6 votes)

- Just a quick question, so in a test it could say find the distance of the other 2 sides of the triangle. Can you find out the other 2 sides using the pythagorean theorem or is there another way to find that out?(15 votes)
- There is no way to do it if you are only given 1 side :((15 votes)

- So, for the Pythagorean Theorem you do a squared plus b squared equals c squared. Why is a+c=b a thing? I don't get it.(0 votes)
- a+c cannot equal b. This is because c is the hypotenuse. Instead, you could do c²-a²=b².(45 votes)

- how can i find the b (the one one the side thats straight)(8 votes)
- you would instead do c^2-a^2=b^2. if you are missing "a" you can also swap those and do c^2 - b^2 = a^2(8 votes)

- I don't exactly understand how to do this, is there an easier way to do this?(14 votes)
- No there is not another way to do this. I SPEND 3 HOURS LEARNING THIS PYTHAGOREAN THEOREM WHEN I DON'T EVEN KNOW HOW TO SQUARE ROOT MY NUMBER ( or spell for a fact this took me about 2 minutes to write down without Grammarly's help :)(1 vote)

- is there a better way to learn this?(13 votes)