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Special Right Triangle Calculator

Geometry

30-60-90 and 45-45-90, one side fixes all

Quick Answer

Special Right Triangle Calculator: 30-60-90 and 45-45-90, one side fixes all. Special Right Triangle Calculator uses standard geometry formulas to compute accurate results instantly.

Triangle type

Known side

Short leg a5.00
Long leg b8.66
Hypotenuse c10.00
Area21.65
90°abc30°60°

Steps

  1. 1短直角边 a（30° 对边）= 5
  2. 2长直角边 b = a×√3 = 5×1.7321 = 8.6603
  3. 3斜边 c = a×2 = 5×2 = 10
  4. 4面积 = a×b÷2 = 21.6506，周长 = 23.6603
Perimeter23.66
  • 30-60-90: sides are a, a√3, 2a — the leg opposite 30° is exactly half the hypotenuse.
  • 45-45-90: isosceles right triangle, legs equal, hypotenuse = leg × √2.
  • Knowing any one side determines the whole triangle — memorize the ratios to skip trigonometry.
  • Common uses: equilateral triangle height (split into 30-60-90), square diagonal (45-45-90).

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How to Use

  1. Enter known values: fill sides, radius or angles in the Special Right Triangle Calculator.
  2. Auto-solve the rest: all unknowns are solved instantly — no manual derivation.
  3. See formula and steps: the result panel shows the formula used and the substitution.
  4. Try another case: change any known value to solve again.

Key Points

  • Special Right Triangle Calculator is a free online geometry tool — open and use, no sign-up.
  • All calculations run locally in your browser; your data never leaves the device.
  • Key capability: 30-60-90 and 45-45-90, one side fixes all.
  • Results come with formulas and reference tables so you can verify every number.

Formula & How It Works

Special Right Triangle Calculator formula

Special Right Triangle Calculator uses standard geometry formulas to compute accurate results instantly.

FAQ

How do I use the Special Right Triangle Calculator?
Open the page and fill in the input fields — results update automatically. 30-60-90 and 45-45-90, one side fixes all.
Are the results accurate?
Yes. Standard formulas and conversion factors are used and verified.
Is it free? Do I need to sign up?
Completely free. No registration, login or download required.
Does it work on mobile?
Yes. The responsive design works on phones, tablets and desktops.
Is my data saved?
No. Everything runs locally in your browser.

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Source & Updates

Based on standard Euclidean geometry formulas. Last updated: 2025-07

Last updated:

Formulas and content on this page are reviewed by the YiJianSuan team. For reference only — official sources prevail.

Maintained and periodically reviewed by the YiJianSuan editorial team — review process in ourEditorial Policy.

Cite this page: YiJianSuan. Special Right Triangle Calculator[EB/OL]. https://www.yijiansuan.com/en/c/geometry/special-right-triangle

Results provided by this tool are for reference only and do not constitute professional advice.