Special Right Triangles Calculator

Special Right Triangles Formula

Worked Example

A 30-60-90 triangle with short leg 5:

1. 30-60-90 sides are in the ratio 1 : √3 : 2 (short leg : long leg : hypotenuse)
2. short leg = 5
3. long leg = short × √3 = 5√3; hypotenuse = 2 × short = 10

Long leg (decimal): 8.660254038 · Hypotenuse (decimal): 10 · Area: 21.65063509 · Perimeter: 23.66025404

Test-day tip

Both ratios are on the SAT reference sheet, but knowing them saves time. An equilateral triangle split in half gives two 30-60-90 triangles, so its height is (side/2)√3.

More Geometry and Trigonometry Calculators

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  Example: A right triangle with legs 6 and 8: Hypotenuse c = 10.

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• Right Triangle Calculator

  sin A = a/c, cos A = b/c, tan A = a/b

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• Unit Circle Calculator

  (cos θ, sin θ) on x² + y² = 1

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  Example: The angle 150°: Point on the unit circle (cos θ, sin θ) = (−√3/2, 1/2).

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• Distance Formula Calculator

  d = √[(x₂ − x₁)² + (y₂ − y₁)²]

  the Pythagorean theorem on the coordinate plane

  Example: The points (1, 2) and (7, 10): Distance d = 10.

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Frequently asked questions

Sources

Last reviewed: 2026-10-15. Factors are stored exactly and computed with 50-digit decimal arithmetic. See how we verify conversion factors.