TriangleVEXQOMIRA / GEOMETRY 02
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.

Three sides (SSS)

s = (a+b+c)/2; A = √[s(s−a)(s−b)(s−c)]

Inputs: Side a (length units); Side b (length units); Side c (length units).

Apply this formula ↗

Base and perpendicular height

A = bh/2

Inputs: Base b (length units); Perpendicular height h (length units).

Apply this formula ↗

Two sides and included angle

c² = a²+b²−2ab cos θ; A = ab sin θ/2

Inputs: Side a (length units); Side b (length units); Included angle θ (degrees).

Apply this formula ↗

Third interior angle

γ = 180°−α−β

Inputs: Angle α (degrees); Angle β (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 included angle in SAS lies between the two entered sides. A sloping side is usually not the perpendicular height.

Reference reading: Triangle at Wolfram MathWorld.