The 30-60-90 Triangle
The 30-60-90 Triangle is a skill on Pengi from Lesson 66: Special Right Triangles in Saxon Math, Course 3.
Key Concepts
Property A 30 60 90 triangle is half of an equilateral triangle. All 30 60 90 triangles have side lengths in the ratio of $1:\sqrt{3}:2$.
Examples If the shortest side of a 30 60 90 triangle is 5 inches, the hypotenuse is $2 \times 5 = 10$ inches. In that same triangle, the side opposite the 60° angle would be $5\sqrt{3}$ inches long. An equilateral triangle with 12 inch sides has a height of $6\sqrt{3}$ inches, found by splitting it into two 30 60 90 triangles.
Explanation Picture an equilateral triangle with all its equal sides. Now, chop it right down the middle! You've just created two 30 60 90 triangles. The shortest leg is always opposite the 30 degree angle, the hypotenuse is simply double the short leg, and the medium leg is the short leg's length times the square root of three.
Common Questions
What is The 30-60-90 Triangle?
The 30-60-90 Triangle is a skill on Pengi from Lesson 66: Special Right Triangles in Saxon Math, Course 3.
What grade level is The 30-60-90 Triangle for?
The 30-60-90 Triangle is part of the Grade 8 Math curriculum, covered in Saxon Math, Course 3. It is designed for students studying Math at the Grade 8 level.
How can I learn The 30-60-90 Triangle?
Pengi offers an AI-guided lesson for The 30-60-90 Triangle that walks you through the key concepts step by step. The lesson is aligned to Saxon Math, Course 3 so the content matches what you see in class.
How do I practice The 30-60-90 Triangle?
After learning the concept, use the Practice mode to work through targeted exercises on The 30-60-90 Triangle. The AI adapts to your level and gives feedback on each answer so you can identify and fix mistakes.
Which textbook covers The 30-60-90 Triangle?
The 30-60-90 Triangle is covered in Saxon Math, Course 3, specifically in Chapter 7: Algebra under Lesson 66: Special Right Triangles. Pengi's lesson is aligned directly to this textbook so you can follow along with your class.
Is The 30-60-90 Triangle free to study on Pengi?
Yes, the core Learn and Practice modes for The 30-60-90 Triangle are available for free on Pengi. No credit card is required to start studying.