30-60-90 Triangle Calculator
Find special right triangle sides from the short leg
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30-60-90 Triangle Formula
short : long : hypotenuse = x : x√3 : 2x
A 30-60-90 triangle has fixed side ratios. Once the short leg is known, the long leg and hypotenuse are determined by multiplying by √3 and 2.
⚠ Enter the short leg, which is opposite the 30° angle. The value must be positive.
How 30-60-90 Triangles Work
This special triangle comes from splitting an equilateral triangle in half. Its angles force a constant side relationship.
Short Leg
Opposite the 30° angle.
Exact Values
Supports common trig ratios.
💡 Example: If the short leg is 5, the long leg is 8.660254 and the hypotenuse is 10.
Applications of 30-60-90 Triangles
Special Right Triangles Exact Trig Values Geometry Construction
Frequently Asked Questions
What is a 30-60-90 triangle calculator?▼
It calculates the long leg and hypotenuse from the short leg of a 30-60-90 triangle.
What is the 30-60-90 side ratio?▼
The ratio is x : x√3 : 2x.
How do I use this calculator?▼
Enter the short leg and click Calculate.
Which side is opposite 30 degrees?▼
The short leg x is opposite the 30° angle.
Where are 30-60-90 triangles used?▼
They are used in exact trig values, geometry, construction, and right triangle problems.
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