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.
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
- OpenStax, Rice University: Precalculus 2eReference material reviewed for the stated method, units, or domain. Confirm that its scope matches your use case. Reviewed 2026-08-14.
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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