Special Right Triangle Calculator
Solve the two special right triangles. Choose 45-45-90 or 30-60-90, enter one side, and the fixed side ratios give you every other side, the area and the perimeter.
How to solve a special right triangle
- Pick the triangle type: 45-45-90 or 30-60-90.
- Choose which side you know and enter its length.
- Read the remaining sides, the area and the perimeter from the ratios.
Examples
45-45-90 from a leg
type 45-45-90, leg = 5
hypotenuse 7.0711, area 12.5
30-60-90 from the short leg
type 30-60-90, short leg = 4
long leg 6.9282, hypotenuse 8, area 13.8564
Frequently asked questions
What are the special right triangles?
They are the 45-45-90 and 30-60-90 triangles. Their angles are fixed, so their side lengths always follow the same ratios no matter the scale.
What are the side ratios?
In a 45-45-90 triangle the sides are in the ratio 1 to 1 to the square root of 2. In a 30-60-90 triangle they are 1 to the square root of 3 to 2 (short, long, hypotenuse).
Which side can I start from?
For 45-45-90 you can enter a leg or the hypotenuse. For 30-60-90 you can enter the short leg, the long leg, or the hypotenuse.
How is the hypotenuse found in a 30-60-90 triangle?
The hypotenuse is always twice the short leg. The long leg is the short leg times the square root of 3, which is about 1.732 times longer.
Are the results exact?
The ratios are exact, but the square roots are irrational, so the side lengths are shown rounded to four decimal places for readability.
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