Pytagorova vetaje jedna z najdôležitejších vecí v matematike, ktorá... Show more
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Updated Mar 23, 2026
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Pytagorova veta: Výpočty a aplikácie
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Čo je Pytagorova veta a prečo ju potrebuješ
Predstav si, že stojíš v rohu miestnosti - stena a podlaha tvoria pravý uhol (presne 90°). Pytagorova veta ti pomôže vypočítať vzdialenosti v takýchto situáciách.
Funguje len s pravouhlými trojuholníkmi - trojuholníkmi, ktoré mají jeden uhol presne 90°. Každý pravouhlý trojuholník má tri strany: dve kratšie odvesny (označujeme ich a a b) a jednu najdlhšiu preponu (c), ktorá leží oproti pravému uhlu.
Základný vzorec je jednoduchý: a² + b² = c². To znamená, že keď si umocníš obe odvesny na druhú a sčítaš ich, dostaneš štvorec prepony.
💡 Tip: Prepona je vždy tá najdlhšia strana! Ak ti vyjde niečo iné, niekde si sa pomýlil.
Ako používať vzorec v praxi
Najprv si vždy over, že máš naozaj pravouhlý trojuholník. Potom si označ strany - prepona je vždy oproti pravému uhlu, odvesny sú tie dve, čo ho tvoria.
Keď hľadáš preponu, vzorec je: c = √. Umocníš obe odvesny, sčítaš ich a z výsledku urobíš druhú odmocninu.
Keď hľadáš odvesnu, vzorec si musíš upraviť: a = √. Vždy odpočítavaš štvorec známej odvesny od štvorca prepony.
💡 Pozor: Nikdy nezabúdaj na odmocňovanie na konci! Častá chyba je, že študenti vypočítajú c² a zabudnú z toho urobiť druhú odmocninu.
Riešené príklady krok za krokom
Príklad 1 - Hľadáme preponu: Odvesny sú 6 cm a 8 cm. Aká je prepona?
- Vzorec: c² = 6² + 8² = 36 + 64 = 100
- Prepona: c = √100 = 10 cm
Príklad 2 - Hľadáme odvesnu: Prepona je 13 cm, jedna odvesna je 5 cm. Aká je druhá odvesna?
- Vzorec: b² = 13² - 5² = 169 - 25 = 144
- Odvesna: b = √144 = 12 cm
Príklad 3 - Rebrík oproti stene: 5-metrový rebrík je 3 metre od steny. Do akej výšky dosahuje?
- Rebrík = prepona (5 m), vzdialenosť od steny = odvesna (3 m)
- Výška² = 5² - 3² = 25 - 9 = 16
- Výška = √16 = 4 metre
💡 Skvelé na zapamätanie: Pytagorejské trojice ako (3,4,5) alebo (5,12,13) ti ušetria čas pri počítaní!
Praktické tipy a časté chyby
Najčastejšie chyby, ktorým sa vyhni: zabúdanie na odmocňovanie, používanie vzorca aj pre nepravouhlé trojuholníky, a výsledok, kde odvesna je dlhšia ako prepona.
Užitočné Pytagorejské trojice na zapamätanie:
- (3, 4, 5) - najzákladnejšia
- (5, 12, 13)
- (8, 15, 17)
Pytagorovu vetu môžeš použiť aj v 3D priestore - napríklad na výpočet uhlopriečky podlahy v miestnosti alebo vzdialenosti v kocke.
Vždy píš jednotky k výsledkom a skontroluj si, či ti prepona vyšla ako najdlhšia strana. Ak nie, niekde je chyba.
💡 Pre skúšku: Najdôležitejšie je vedieť vzorec a² + b² = c², rozoznať pravouhlý trojuholník a nezabudnúť odmocniť výsledok!
We thought you’d never ask...
What is the Knowunity AI companion?
Our AI companion is specifically built for the needs of students. Based on the millions of content pieces we have on the platform we can provide truly meaningful and relevant answers to students. But its not only about answers, the companion is even more about guiding students through their daily learning challenges, with personalised study plans, quizzes or content pieces in the chat and 100% personalisation based on the students skills and developments.
Where can I download the Knowunity app?
You can download the app in the Google Play Store and in the Apple App Store.
Is Knowunity really free of charge?
That's right! Enjoy free access to study content, connect with fellow students, and get instant help – all at your fingertips.
Most popular content in Matematika
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4.6/5
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4.7/5
Google Play
The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.
Stefan S
iOS user
This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.
Samantha Klich
Android user
Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.
Anna
iOS user
I think it’s very much worth it and you’ll end up using it a lot once you get the hang of it and even after looking at others notes you can still ask your Artificial intelligence buddy the question and ask to simplify it if you still don’t get it!!! In the end I think it’s worth it 😊👍 ⚠️Also DID I MENTION ITS FREEE YOU DON’T HAVE TO PAY FOR ANYTHING AND STILL GET YOUR GRADES IN PERFECTLY❗️❗️⚠️
Thomas R
iOS user
Knowunity is the BEST app I’ve used in a minute. This is not an ai review or anything this is genuinely coming from a 7th grade student (I know 2011 im young) but dude this app is a 10/10 i have maintained a 3.8 gpa and have plenty of time for gaming. I love it and my mom is just happy I got good grades
Brad T
Android user
Not only did it help me find the answer but it also showed me alternative ways to solve it. I was horrible in math and science but now I have an a in both subjects. Thanks for the help🤍🤍
David K
iOS user
The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!
Sudenaz Ocak
Android user
In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.
Greenlight Bonnie
Android user
I found this app a couple years ago and it has only gotten better since then. I really love it because it can help with written questions and photo questions. Also, it can find study guides that other people have made as well as flashcard sets and practice tests. The free version is also amazing for students who might not be able to afford it. Would 100% recommend
Aubrey
iOS user
Best app if you're in Highschool or Junior high. I have been using this app for 2 school years and it's the best, it's good if you don't have anyone to help you with school work.😋🩷🎀
Marco B
iOS user
THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE Knowunity AI. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH 😍😁😲🤑💗✨🎀😮
Elisha
iOS user
This app is phenomenal down to the correct info and the various topics you can study! I greatly recommend it for people who struggle with procrastination and those who need homework help. It has been perfectly accurate for world 1 history as far as I’ve seen! Geometry too!
Paul T
iOS user
The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.
Stefan S
iOS user
This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.
Samantha Klich
Android user
Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.
Anna
iOS user
I think it’s very much worth it and you’ll end up using it a lot once you get the hang of it and even after looking at others notes you can still ask your Artificial intelligence buddy the question and ask to simplify it if you still don’t get it!!! In the end I think it’s worth it 😊👍 ⚠️Also DID I MENTION ITS FREEE YOU DON’T HAVE TO PAY FOR ANYTHING AND STILL GET YOUR GRADES IN PERFECTLY❗️❗️⚠️
Thomas R
iOS user
Knowunity is the BEST app I’ve used in a minute. This is not an ai review or anything this is genuinely coming from a 7th grade student (I know 2011 im young) but dude this app is a 10/10 i have maintained a 3.8 gpa and have plenty of time for gaming. I love it and my mom is just happy I got good grades
Brad T
Android user
Not only did it help me find the answer but it also showed me alternative ways to solve it. I was horrible in math and science but now I have an a in both subjects. Thanks for the help🤍🤍
David K
iOS user
The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!
Sudenaz Ocak
Android user
In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.
Greenlight Bonnie
Android user
I found this app a couple years ago and it has only gotten better since then. I really love it because it can help with written questions and photo questions. Also, it can find study guides that other people have made as well as flashcard sets and practice tests. The free version is also amazing for students who might not be able to afford it. Would 100% recommend
Aubrey
iOS user
Best app if you're in Highschool or Junior high. I have been using this app for 2 school years and it's the best, it's good if you don't have anyone to help you with school work.😋🩷🎀
Marco B
iOS user
THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE Knowunity AI. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH 😍😁😲🤑💗✨🎀😮
Elisha
iOS user
This app is phenomenal down to the correct info and the various topics you can study! I greatly recommend it for people who struggle with procrastination and those who need homework help. It has been perfectly accurate for world 1 history as far as I’ve seen! Geometry too!
Paul T
iOS user
Pytagorova veta: Výpočty a aplikácie
Pytagorova veta je jedna z najdôležitejších vecí v matematike, ktorá ti pomôže vyriešiť problémy s pravouhlými trojuholníkmi. Či už počítaš výšku rebríka opreteho o stenu alebo uhlopriečku tvojej izby, táto veta ti bude super užitočná!
Čo je Pytagorova veta a prečo ju potrebuješ
Predstav si, že stojíš v rohu miestnosti - stena a podlaha tvoria pravý uhol (presne 90°). Pytagorova veta ti pomôže vypočítať vzdialenosti v takýchto situáciách.
Funguje len s pravouhlými trojuholníkmi - trojuholníkmi, ktoré mají jeden uhol presne 90°. Každý pravouhlý trojuholník má tri strany: dve kratšie odvesny (označujeme ich a a b) a jednu najdlhšiu preponu (c), ktorá leží oproti pravému uhlu.
Základný vzorec je jednoduchý: a² + b² = c². To znamená, že keď si umocníš obe odvesny na druhú a sčítaš ich, dostaneš štvorec prepony.
💡 Tip: Prepona je vždy tá najdlhšia strana! Ak ti vyjde niečo iné, niekde si sa pomýlil.
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Ako používať vzorec v praxi
Najprv si vždy over, že máš naozaj pravouhlý trojuholník. Potom si označ strany - prepona je vždy oproti pravému uhlu, odvesny sú tie dve, čo ho tvoria.
Keď hľadáš preponu, vzorec je: c = √. Umocníš obe odvesny, sčítaš ich a z výsledku urobíš druhú odmocninu.
Keď hľadáš odvesnu, vzorec si musíš upraviť: a = √. Vždy odpočítavaš štvorec známej odvesny od štvorca prepony.
💡 Pozor: Nikdy nezabúdaj na odmocňovanie na konci! Častá chyba je, že študenti vypočítajú c² a zabudnú z toho urobiť druhú odmocninu.
Sign up to see the contentIt's free!
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Riešené príklady krok za krokom
Príklad 1 - Hľadáme preponu: Odvesny sú 6 cm a 8 cm. Aká je prepona?
- Vzorec: c² = 6² + 8² = 36 + 64 = 100
- Prepona: c = √100 = 10 cm
Príklad 2 - Hľadáme odvesnu: Prepona je 13 cm, jedna odvesna je 5 cm. Aká je druhá odvesna?
- Vzorec: b² = 13² - 5² = 169 - 25 = 144
- Odvesna: b = √144 = 12 cm
Príklad 3 - Rebrík oproti stene: 5-metrový rebrík je 3 metre od steny. Do akej výšky dosahuje?
- Rebrík = prepona (5 m), vzdialenosť od steny = odvesna (3 m)
- Výška² = 5² - 3² = 25 - 9 = 16
- Výška = √16 = 4 metre
💡 Skvelé na zapamätanie: Pytagorejské trojice ako (3,4,5) alebo (5,12,13) ti ušetria čas pri počítaní!
Sign up to see the contentIt's free!
Access to all documents
Improve your grades
Join milions of students
Praktické tipy a časté chyby
Najčastejšie chyby, ktorým sa vyhni: zabúdanie na odmocňovanie, používanie vzorca aj pre nepravouhlé trojuholníky, a výsledok, kde odvesna je dlhšia ako prepona.
Užitočné Pytagorejské trojice na zapamätanie:
- (3, 4, 5) - najzákladnejšia
- (5, 12, 13)
- (8, 15, 17)
Pytagorovu vetu môžeš použiť aj v 3D priestore - napríklad na výpočet uhlopriečky podlahy v miestnosti alebo vzdialenosti v kocke.
Vždy píš jednotky k výsledkom a skontroluj si, či ti prepona vyšla ako najdlhšia strana. Ak nie, niekde je chyba.
💡 Pre skúšku: Najdôležitejšie je vedieť vzorec a² + b² = c², rozoznať pravouhlý trojuholník a nezabudnúť odmocniť výsledok!
Sign up to see the contentIt's free!
Access to all documents
Improve your grades
Join milions of students
Sign up to see the contentIt's free!
Access to all documents
Improve your grades
Join milions of students
Sign up to see the contentIt's free!
Access to all documents
Improve your grades
Join milions of students
We thought you’d never ask...
What is the Knowunity AI companion?
Our AI companion is specifically built for the needs of students. Based on the millions of content pieces we have on the platform we can provide truly meaningful and relevant answers to students. But its not only about answers, the companion is even more about guiding students through their daily learning challenges, with personalised study plans, quizzes or content pieces in the chat and 100% personalisation based on the students skills and developments.
Where can I download the Knowunity app?
You can download the app in the Google Play Store and in the Apple App Store.
Is Knowunity really free of charge?
That's right! Enjoy free access to study content, connect with fellow students, and get instant help – all at your fingertips.
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Most popular content in Matematika
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Can't find what you're looking for? Explore other subjects.
Students love us — and so will you.
4.6/5
App Store
4.7/5
Google Play
The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.
Stefan S
iOS user
This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.
Samantha Klich
Android user
Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.
Anna
iOS user
I think it’s very much worth it and you’ll end up using it a lot once you get the hang of it and even after looking at others notes you can still ask your Artificial intelligence buddy the question and ask to simplify it if you still don’t get it!!! In the end I think it’s worth it 😊👍 ⚠️Also DID I MENTION ITS FREEE YOU DON’T HAVE TO PAY FOR ANYTHING AND STILL GET YOUR GRADES IN PERFECTLY❗️❗️⚠️
Thomas R
iOS user
Knowunity is the BEST app I’ve used in a minute. This is not an ai review or anything this is genuinely coming from a 7th grade student (I know 2011 im young) but dude this app is a 10/10 i have maintained a 3.8 gpa and have plenty of time for gaming. I love it and my mom is just happy I got good grades
Brad T
Android user
Not only did it help me find the answer but it also showed me alternative ways to solve it. I was horrible in math and science but now I have an a in both subjects. Thanks for the help🤍🤍
David K
iOS user
The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!
Sudenaz Ocak
Android user
In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.
Greenlight Bonnie
Android user
I found this app a couple years ago and it has only gotten better since then. I really love it because it can help with written questions and photo questions. Also, it can find study guides that other people have made as well as flashcard sets and practice tests. The free version is also amazing for students who might not be able to afford it. Would 100% recommend
Aubrey
iOS user
Best app if you're in Highschool or Junior high. I have been using this app for 2 school years and it's the best, it's good if you don't have anyone to help you with school work.😋🩷🎀
Marco B
iOS user
THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE Knowunity AI. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH 😍😁😲🤑💗✨🎀😮
Elisha
iOS user
This app is phenomenal down to the correct info and the various topics you can study! I greatly recommend it for people who struggle with procrastination and those who need homework help. It has been perfectly accurate for world 1 history as far as I’ve seen! Geometry too!
Paul T
iOS user
The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.
Stefan S
iOS user
This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.
Samantha Klich
Android user
Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.
Anna
iOS user
I think it’s very much worth it and you’ll end up using it a lot once you get the hang of it and even after looking at others notes you can still ask your Artificial intelligence buddy the question and ask to simplify it if you still don’t get it!!! In the end I think it’s worth it 😊👍 ⚠️Also DID I MENTION ITS FREEE YOU DON’T HAVE TO PAY FOR ANYTHING AND STILL GET YOUR GRADES IN PERFECTLY❗️❗️⚠️
Thomas R
iOS user
Knowunity is the BEST app I’ve used in a minute. This is not an ai review or anything this is genuinely coming from a 7th grade student (I know 2011 im young) but dude this app is a 10/10 i have maintained a 3.8 gpa and have plenty of time for gaming. I love it and my mom is just happy I got good grades
Brad T
Android user
Not only did it help me find the answer but it also showed me alternative ways to solve it. I was horrible in math and science but now I have an a in both subjects. Thanks for the help🤍🤍
David K
iOS user
The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!
Sudenaz Ocak
Android user
In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.
Greenlight Bonnie
Android user
I found this app a couple years ago and it has only gotten better since then. I really love it because it can help with written questions and photo questions. Also, it can find study guides that other people have made as well as flashcard sets and practice tests. The free version is also amazing for students who might not be able to afford it. Would 100% recommend
Aubrey
iOS user
Best app if you're in Highschool or Junior high. I have been using this app for 2 school years and it's the best, it's good if you don't have anyone to help you with school work.😋🩷🎀
Marco B
iOS user
THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE Knowunity AI. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH 😍😁😲🤑💗✨🎀😮
Elisha
iOS user
This app is phenomenal down to the correct info and the various topics you can study! I greatly recommend it for people who struggle with procrastination and those who need homework help. It has been perfectly accurate for world 1 history as far as I’ve seen! Geometry too!
Paul T
iOS user