About the 30-60-90 Triangle
The short leg is opposite the 30 degree angle.
The long leg is √3 times the short leg.
The hypotenuse is twice the short leg.
These fixed ratios make 30-60-90 triangles common in school geometry and trigonometry.
Calculate the area and all three side lengths of a 30-60-90 special right triangle from its short leg.
Fill in the details and click Calculate to see your results.
The short leg is opposite the 30 degree angle.
The long leg is √3 times the short leg.
The hypotenuse is twice the short leg.
These fixed ratios make 30-60-90 triangles common in school geometry and trigonometry.
| Short Leg | 5 cm |
| Triangle Area | 21.6506 |
| Long Leg | 8.66025 |
| Hypotenuse | 10 |
The long leg is about 8.66025 cm, the hypotenuse is 10 cm and the area is about 21.6506 square centimetres.
Try this example →The ratio of the short leg, long leg and hypotenuse is 1:√3:2.
Divide the hypotenuse by 2 to get the short leg, then use the calculator.
Divide the long leg by √3 to obtain the short leg.
If x is the short leg, area equals x²√3/2.