Special Right Triangle Calculator
Two right triangles have side ratios so fixed that one side determines them all: the isosceles 45-45-90 (1 : 1 : √2) and the 30-60-90 (1 : √3 : 2). Enter the side you know and get the complete triangle.
Results
Formula
How to use this calculator
- Pick the triangle type.
- Say which side you know and enter its length.
- Press Calculate — the ratio scales to your triangle.
Worked example
A 45-45-90 triangle with legs of 5.
- The legs are equal: both 5.
- Hypotenuse: 5 × √2 ≈ 7.071.
Result: Sides are 5, 5 and ≈ 7.071.
Frequently asked questions
Where does the 30-60-90 ratio come from?
Cut an equilateral triangle in half. The halves are 30-60-90 triangles whose sides must follow 1 : √3 : 2 by the Pythagorean theorem.
Which leg is “short” in a 30-60-90?
The one opposite the 30° angle. It is always exactly half the hypotenuse.
Why are these two triangles “special”?
Their angles are the ones with exact, memorable trig values (multiples of √2 and √3), so textbooks and standardized tests use them constantly.
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