Special Right Triangles Calculator

Use the Special Right Triangles Calculator for a transparent, instant calculation with validated inputs and cited sources. For a query such as “special triangles”, enter the matching values and units below and review the stated assumptions.

Inputs

Results update as you type.

This field is required.

Result

Results update as you type.

45-45-90 hypotenuse
7.0710678119
30-60-90 long leg
8.6602540378
30-60-90 hypotenuse
10

How to use this calculator

Enter the requested values and units.

Review the assumptions and any warnings shown with the result.

Use the result together with the cited source and your real-world requirements.

Formula

Return the 45-45-90 relation x:x:x√2 and the 30-60-90 short-leg relation x:x√3:2x.

Worked example

Worked example: Inputs: 45° leg and 30-60-90 short leg: 5. Outputs: 45-45-90 hypotenuse: 7.071068; 30-60-90 long leg: 8.660254; 30-60-90 hypotenuse: 10.

Assumptions and limits

  • The result depends on the values, units, and assumptions entered. It does not infer missing context.

Sources

Related calculators

Frequently asked questions

How does the Special Right Triangles Calculator work?

Return the 45-45-90 relation x:x:x√2 and the 30-60-90 short-leg relation x:x√3:2x.

What should I enter?

45° leg and 30-60-90 short leg

What should I verify?

Review the assumptions and any warnings shown with the result. The result depends on the values, units, and assumptions entered. It does not infer missing context.

Last updated 2026-08-14 · math-special-right-triangles-v1 · opportunity-content-2026-08-14 · Trusty Calculator Editorial Team