🔺 Special Right Triangles Calculator
Calculate 30-60-90 and 45-45-90 triangle properties
How to Use This Calculator
Select Triangle Type
Choose between 30-60-90 or 45-45-90 triangle.
Select Known Side
Choose which side you know (short, medium, hypotenuse for 30-60-90; leg or hypotenuse for 45-45-90).
Enter Value
Input the length of the known side.
Calculate
Click "Calculate" to find all remaining sides, angles, area, and perimeter.
Formula
30-60-90 Triangle
Ratio: 1 : √3 : 2
If short side = a:
- Medium side = a√3
- Hypotenuse = 2a
45-45-90 Triangle
Ratio: 1 : 1 : √2
If leg = a:
- Both legs = a
- Hypotenuse = a√2
About Special Right Triangles Calculator
The Special Right Triangles Calculator finds all properties of 30-60-90 and 45-45-90 triangles. These triangles have fixed angle ratios and side relationships, making calculations straightforward.
When to Use This Calculator
- Geometry: Solve special right triangle problems
- Trigonometry: Understand special angle relationships
- Construction: Calculate measurements for special angles
- Education: Learn about special triangles
Why Use Our Calculator?
- ✅ Both Types: Handles 30-60-90 and 45-45-90 triangles
- ✅ Complete Calculations: Finds all properties from one side
- ✅ Accurate: Uses exact mathematical ratios
- ✅ Educational: Helps understand special triangle properties
- ✅ Free: No registration required
Frequently Asked Questions
What are special right triangles?
Special right triangles have fixed angle measures and side ratios. The two main types are 30-60-90 (angles 30°, 60°, 90°) and 45-45-90 (angles 45°, 45°, 90°).
Why are these triangles special?
They have consistent side ratios that make calculations easy: 30-60-90 has ratio 1:√3:2, and 45-45-90 has ratio 1:1:√2.
Can I use this for non-special triangles?
No, this calculator is specifically for 30-60-90 and 45-45-90 triangles. Use the Right Triangle Calculator for other right triangles.