A comprehensive guide to special right triangles 45-45-90and 30-60-90,...
Algebra 2200 views·Updated Jul 11, 2026·1 pageFun Guide to Special Right Triangles: 45-45-90 and 30-60-90
Maria Hernandez@mariahernandez
1
of 1
Special Right Triangles: Key Relationships and Calculations
The first page introduces two fundamental special right triangles: the 45-45-90 and 30-60-90 triangles, along with their essential properties and calculations. These triangles have unique characteristics that make them particularly useful in geometric problem-solving.
Definition: A 45-45-90 triangle is a right triangle with two 45-degree angles and one 90-degree angle, where both legs are equal in length.
Highlight: For a 45-45-90 triangle, if the legs are length x, the hypotenuse will always be x√2.
Example: In a 45-45-90 triangle with legs of 5 units, the hypotenuse would be 5√2 ≈ 7.1 units.
Vocabulary: The "leg" refers to either of the two sides that form the right angle in a right triangle, while the "hypotenuse" is the longest side opposite the right angle.
Definition: A 30-60-90 triangle has angles of 30, 60, and 90 degrees, with sides following a specific ratio pattern.
Example: In a 30-60-90 triangle with a short leg of 14 units, the long leg would be 14√3 ≈ 24.2 units, and the hypotenuse would be 28 units.
Highlight: For a 30-60-90 triangle, if the shortest leg is x, then the long leg is x√3, and the hypotenuse is 2x.
We thought you’d never ask...
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.
You can download the app in the Google Play Store and in the Apple App Store.
That's right! Enjoy free access to study content, connect with fellow students, and get instant help – all at your fingertips.
Similar Content
TrigonometryMost popular content: Special Right Triangles
2Most popular content in Algebra 2
9Algebra 2Properties of Real Numbers
Notes about the topic
1412
Algebra 21.2 - Intro to Sets
Sets, subsets, set builder notation
10th372
Algebra 1Linear Function: Solving Linear Equations in 1 Variable
Study note on linear equations with one variable, rules on linear equations, examples on simple linear equations, algebra 2, algebra 1
9th3341
Algebra 2Midterm Study Guide: Review of the First Half of the Course
Simple review notes and examples for the first half of the algebra 2 course! Not all classes teach the content in the same order, but this study guide should have most of the more basic concepts from algebra 2!
9th1,207120
Algebra 2Rational Exponents
Writing rational exponents in radical form and exponential form. And even and odd radicals
1535
Algebra 2math 3 final exam study guide
covers all content learned in tj math 3 (algebra 2)
10th1,660180
Algebra 2Absolute value functions
Steps to to solve absolute value functions
980
Algebra 2Transfermations - Quadratic Functions
Learn how to identify the vertex, direction, and maximum or minimum for different parabolas in vertex form.
10th640
Algebra 2(honors) Algebra 2 Trigonometry
Unit circle trig ranging from simple right triangle trig to modeling with sinusoids and more complex story problems
9th45333
Most popular content
9O
AP US HistoryOrigins and Dynamics of the Columbian Exchange
Analyze the ecological and economic motivations behind the initial transfer of goods, people, and diseases between the Old and New Worlds.
9th3,1280
I
AP US HistoryIntroduction to Early Cultural Interactions
Analyze the initial social and religious encounters between Europeans, Africans, and Indigenous peoples in the colonial Americas.
9th2,7730
O
AP World HistoryOrigins of Ancient River Civilizations
Analyze the environmental factors and technological innovations that led to the rise of early states in Mesopotamia, Egypt, and the Indus Valley.
9th3,1870
M
AP US HistoryMotivations for European Exploration
Analyze the economic, religious, and political factors that drove European powers to the Americas during the 15th and 16th centuries.
9th1,7780
F
AP PsychologyFoundations of Ethical Guidelines in Research
Practice the core principles of the APA ethical code including informed consent, debriefing, and the role of Institutional Review Boards.
9th1,3360
I
AP US HistoryIntroduction to Native American Societies
Examine the diverse social, political, and economic structures of North American indigenous groups prior to European contact.
9th1,1100
I
AP US HistoryIntroduction to the Spanish Encomienda System
Explore the fundamental economic and social structures of the Spanish colonial system, focusing on the encomienda and the casta social hierarchy.
9th8890
I
AP BiologyIntroduction to Biological Elements of Life
Practice identifying the essential elements including carbon, nitrogen, phosphorus, and sulfur that compose biological macromolecules.
9th1,7410
O
AP US Government & PoliticsOrigins of the Articles of Confederation
Practice identifying the motivations for a weak central government and the specific powers granted to the states under the first U.S. constitution.
9th9370
Students love us — and so will you.
4.6/5App Store
4.7/5Google 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 SiOS 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 KlichAndroid 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.
AnnaiOS user
Algebra 2200 views·Updated Jul 11, 2026·1 pageFun Guide to Special Right Triangles: 45-45-90 and 30-60-90
Maria Hernandez@mariahernandez
A comprehensive guide to special right triangles 45-45-90 and 30-60-90, focusing on their unique properties and methods for calculating hypotenuse and finding leg lengths in special triangles. The guide covers essential formulas, relationships between sides, and practical applications in...
1
of 1
Sign up to see the content. It's free!
- Access to all documents
- Improve your grades
- Join milions of students
Special Right Triangles: Key Relationships and Calculations
The first page introduces two fundamental special right triangles: the 45-45-90 and 30-60-90 triangles, along with their essential properties and calculations. These triangles have unique characteristics that make them particularly useful in geometric problem-solving.
Definition: A 45-45-90 triangle is a right triangle with two 45-degree angles and one 90-degree angle, where both legs are equal in length.
Highlight: For a 45-45-90 triangle, if the legs are length x, the hypotenuse will always be x√2.
Example: In a 45-45-90 triangle with legs of 5 units, the hypotenuse would be 5√2 ≈ 7.1 units.
Vocabulary: The "leg" refers to either of the two sides that form the right angle in a right triangle, while the "hypotenuse" is the longest side opposite the right angle.
Definition: A 30-60-90 triangle has angles of 30, 60, and 90 degrees, with sides following a specific ratio pattern.
Example: In a 30-60-90 triangle with a short leg of 14 units, the long leg would be 14√3 ≈ 24.2 units, and the hypotenuse would be 28 units.
Highlight: For a 30-60-90 triangle, if the shortest leg is x, then the long leg is x√3, and the hypotenuse is 2x.
We thought you’d never ask...
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.
You can download the app in the Google Play Store and in the Apple App Store.
That's right! Enjoy free access to study content, connect with fellow students, and get instant help – all at your fingertips.
Similar Content
Most popular content: Special Right Triangles
2Most popular content in Algebra 2
9Algebra 2Properties of Real Numbers
Notes about the topic
1412
Algebra 21.2 - Intro to Sets
Sets, subsets, set builder notation
10th372
Algebra 1Linear Function: Solving Linear Equations in 1 Variable
Study note on linear equations with one variable, rules on linear equations, examples on simple linear equations, algebra 2, algebra 1
9th3341
Algebra 2Midterm Study Guide: Review of the First Half of the Course
Simple review notes and examples for the first half of the algebra 2 course! Not all classes teach the content in the same order, but this study guide should have most of the more basic concepts from algebra 2!
9th1,207120
Algebra 2Rational Exponents
Writing rational exponents in radical form and exponential form. And even and odd radicals
1535
Algebra 2math 3 final exam study guide
covers all content learned in tj math 3 (algebra 2)
10th1,660180
Algebra 2Absolute value functions
Steps to to solve absolute value functions
980
Algebra 2Transfermations - Quadratic Functions
Learn how to identify the vertex, direction, and maximum or minimum for different parabolas in vertex form.
10th640
Algebra 2(honors) Algebra 2 Trigonometry
Unit circle trig ranging from simple right triangle trig to modeling with sinusoids and more complex story problems
9th45333
Most popular content
9O
AP US HistoryOrigins and Dynamics of the Columbian Exchange
Analyze the ecological and economic motivations behind the initial transfer of goods, people, and diseases between the Old and New Worlds.
9th3,1280
I
AP US HistoryIntroduction to Early Cultural Interactions
Analyze the initial social and religious encounters between Europeans, Africans, and Indigenous peoples in the colonial Americas.
9th2,7730
O
AP World HistoryOrigins of Ancient River Civilizations
Analyze the environmental factors and technological innovations that led to the rise of early states in Mesopotamia, Egypt, and the Indus Valley.
9th3,1870
M
AP US HistoryMotivations for European Exploration
Analyze the economic, religious, and political factors that drove European powers to the Americas during the 15th and 16th centuries.
9th1,7780
F
AP PsychologyFoundations of Ethical Guidelines in Research
Practice the core principles of the APA ethical code including informed consent, debriefing, and the role of Institutional Review Boards.
9th1,3360
I
AP US HistoryIntroduction to Native American Societies
Examine the diverse social, political, and economic structures of North American indigenous groups prior to European contact.
9th1,1100
I
AP US HistoryIntroduction to the Spanish Encomienda System
Explore the fundamental economic and social structures of the Spanish colonial system, focusing on the encomienda and the casta social hierarchy.
9th8890
I
AP BiologyIntroduction to Biological Elements of Life
Practice identifying the essential elements including carbon, nitrogen, phosphorus, and sulfur that compose biological macromolecules.
9th1,7410
O
AP US Government & PoliticsOrigins of the Articles of Confederation
Practice identifying the motivations for a weak central government and the specific powers granted to the states under the first U.S. constitution.
9th9370
Students love us — and so will you.
4.6/5App Store
4.7/5Google 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 SiOS 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 KlichAndroid 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.
AnnaiOS user