Right triangleVEXQOMIRA / GEOMETRY 03
Right triangle Vexqomira

Formulas, without the guesswork.

Choose a relationship from the measurements you know. The variable names below belong to each calculator; a letter can have a different role in another method. π is evaluated using the browser’s full numerical constant, rather than replacing it with 3.14.

Two perpendicular legs

c = √(a²+b²); A = ab/2

Inputs: Leg a (length units); Leg b (length units).

Apply this formula ↗

Hypotenuse and one leg

b = √(c²−a²)

Inputs: Hypotenuse c (length units); Leg a (length units).

Apply this formula ↗

Adjacent leg and acute angle

a = b tan θ

Inputs: Adjacent leg b (length units); Acute angle θ (degrees).

Apply this formula ↗

Hypotenuse and acute angle

a = c sin θ; b = c cos θ

Inputs: Hypotenuse c (length units); Acute angle θ (degrees).

Apply this formula ↗

Reading the notation

√ means a square root, ∛ means a cube root, and a superscript ² or ³ means a square or cube. Sine, cosine and tangent use angles converted from entered degrees. Where an inverse trigonometric function is used, its displayed angle is converted back to degrees. The ellipse perimeter is approximate; other formula labels describe the ideal mathematical model.

The hypotenuse must exceed either leg. Acute-angle calculators require an angle strictly between 0 and 90 degrees.

Reference reading: Right triangle at Wolfram MathWorld.