Special Right Triangles Calculator
How It Works
This special right triangles calculator uses established formulas to provide accurate results.
The basic rule:
- 45-45-90 ratio: 1 : 1 : √2
- 30-60-90 ratio: 1 : √3 : 2
- Hypotenuse (45-45-90) = leg × √2
- Short leg (30-60-90) = hypotenuse / 2
Results are estimates. Consult a professional for critical decisions.
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Explore Allday Everyday Math →Frequently Asked Questions
What are the ratios for a 45-45-90 triangle?
In a 45-45-90 triangle, the two legs are equal and the hypotenuse is leg × √2. The ratio is 1 : 1 : √2.
What are the ratios for a 30-60-90 triangle?
In a 30-60-90 triangle, the side opposite 30° (short leg) has ratio 1, the side opposite 60° (long leg) has ratio √3, and the hypotenuse has ratio 2. The ratio is 1 : √3 : 2.
Why are special right triangles important?
Special right triangles appear frequently in geometry, trigonometry, and standardized tests. Memorizing the ratios allows you to find missing sides instantly without using the Pythagorean theorem or trigonometric functions.
How do special triangles relate to the unit circle?
The 30-60-90 and 45-45-90 triangles are used to derive the exact values of sine, cosine, and tangent for 30°, 45°, and 60° on the unit circle.