Pytagorova vetaje jedna z najdôležitejších vecí v matematike, ktorá... Show more
Matematika
Slovenský jazyk
AngličtinaSign up to see the contentIt's free!
Access to all documents
Improve your grades
Join milions of students
125
•
Updated Mar 23, 2026
•
Pytagorova veta: Výpočty a aplikácie
1 / 7
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 a student-focused AI tool that offers more than just answers. Built on millions of Knowunity resources, it provides relevant information, personalised study plans, quizzes, and content directly in the chat, adapting to your individual learning journey.
Where can I download the Knowunity app?
You can download the app from Google Play Store and 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
Most popular content
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
Best app on earth! no words because it’s too good
Thomas R
iOS user
Just amazing. Let's me revise 10x better, this app is a quick 10/10. I highly recommend it to anyone. I can watch and search for notes. I can save them in the subject folder. I can revise it any time when I come back. If you haven't tried this app, you're really missing out.
Basil
Android user
This app has made me feel so much more confident in my exam prep, not only through boosting my own self confidence through the features that allow you to connect with others and feel less alone, but also through the way the app itself is centred around making you feel better. It is easy to navigate, fun to use, and helpful to anyone struggling in absolutely any way.
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
very reliable app to help and grow your ideas of Maths, English and other related topics in your works. please use this app if your struggling in areas, this app is key for that. wish I'd of done a review before. and it's also free so don't worry about that.
Rohan U
Android user
I know a lot of apps use fake accounts to boost their reviews but this app deserves it all. Originally I was getting 4 in my English exams and this time I got a grade 7. I didn’t even know about this app three days until the exam and it has helped A LOT. Please actually trust me and use it as I’m sure you too will see developments.
Xander S
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 apps acc the goat. I find revision so boring but this app makes it so easy to organize it all and then you can ask the freeeee ai to test yourself so good and you can easily upload your own stuff. highly recommend as someone taking mocks now
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
Best app on earth! no words because it’s too good
Thomas R
iOS user
Just amazing. Let's me revise 10x better, this app is a quick 10/10. I highly recommend it to anyone. I can watch and search for notes. I can save them in the subject folder. I can revise it any time when I come back. If you haven't tried this app, you're really missing out.
Basil
Android user
This app has made me feel so much more confident in my exam prep, not only through boosting my own self confidence through the features that allow you to connect with others and feel less alone, but also through the way the app itself is centred around making you feel better. It is easy to navigate, fun to use, and helpful to anyone struggling in absolutely any way.
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
very reliable app to help and grow your ideas of Maths, English and other related topics in your works. please use this app if your struggling in areas, this app is key for that. wish I'd of done a review before. and it's also free so don't worry about that.
Rohan U
Android user
I know a lot of apps use fake accounts to boost their reviews but this app deserves it all. Originally I was getting 4 in my English exams and this time I got a grade 7. I didn’t even know about this app three days until the exam and it has helped A LOT. Please actually trust me and use it as I’m sure you too will see developments.
Xander S
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 apps acc the goat. I find revision so boring but this app makes it so easy to organize it all and then you can ask the freeeee ai to test yourself so good and you can easily upload your own stuff. highly recommend as someone taking mocks now
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.
Sign up to see the contentIt's free!
Access to all documents
Improve your grades
Join milions of students
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!
Access to all documents
Improve your grades
Join milions of students
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 a student-focused AI tool that offers more than just answers. Built on millions of Knowunity resources, it provides relevant information, personalised study plans, quizzes, and content directly in the chat, adapting to your individual learning journey.
Where can I download the Knowunity app?
You can download the app from Google Play Store and 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.
0
Smart Tools NEW
Transform this note into: ✓ 50+ Practice Questions ✓ Interactive Flashcards ✓ Full Mock Exam ✓ Essay Outlines
Mock Exam
Quiz
Flashcards
Essay
Most popular content in Matematika
Most popular content
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
Best app on earth! no words because it’s too good
Thomas R
iOS user
Just amazing. Let's me revise 10x better, this app is a quick 10/10. I highly recommend it to anyone. I can watch and search for notes. I can save them in the subject folder. I can revise it any time when I come back. If you haven't tried this app, you're really missing out.
Basil
Android user
This app has made me feel so much more confident in my exam prep, not only through boosting my own self confidence through the features that allow you to connect with others and feel less alone, but also through the way the app itself is centred around making you feel better. It is easy to navigate, fun to use, and helpful to anyone struggling in absolutely any way.
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
very reliable app to help and grow your ideas of Maths, English and other related topics in your works. please use this app if your struggling in areas, this app is key for that. wish I'd of done a review before. and it's also free so don't worry about that.
Rohan U
Android user
I know a lot of apps use fake accounts to boost their reviews but this app deserves it all. Originally I was getting 4 in my English exams and this time I got a grade 7. I didn’t even know about this app three days until the exam and it has helped A LOT. Please actually trust me and use it as I’m sure you too will see developments.
Xander S
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 apps acc the goat. I find revision so boring but this app makes it so easy to organize it all and then you can ask the freeeee ai to test yourself so good and you can easily upload your own stuff. highly recommend as someone taking mocks now
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
Best app on earth! no words because it’s too good
Thomas R
iOS user
Just amazing. Let's me revise 10x better, this app is a quick 10/10. I highly recommend it to anyone. I can watch and search for notes. I can save them in the subject folder. I can revise it any time when I come back. If you haven't tried this app, you're really missing out.
Basil
Android user
This app has made me feel so much more confident in my exam prep, not only through boosting my own self confidence through the features that allow you to connect with others and feel less alone, but also through the way the app itself is centred around making you feel better. It is easy to navigate, fun to use, and helpful to anyone struggling in absolutely any way.
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
very reliable app to help and grow your ideas of Maths, English and other related topics in your works. please use this app if your struggling in areas, this app is key for that. wish I'd of done a review before. and it's also free so don't worry about that.
Rohan U
Android user
I know a lot of apps use fake accounts to boost their reviews but this app deserves it all. Originally I was getting 4 in my English exams and this time I got a grade 7. I didn’t even know about this app three days until the exam and it has helped A LOT. Please actually trust me and use it as I’m sure you too will see developments.
Xander S
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 apps acc the goat. I find revision so boring but this app makes it so easy to organize it all and then you can ask the freeeee ai to test yourself so good and you can easily upload your own stuff. highly recommend as someone taking mocks now
Paul T
iOS user