Triangle Side Calculator

This calculator relies on fundamental trigonometric identities and geometric theorems depending on your known inputs. When you know two sides and the included angle (SAS), the tool uses the Law of Cosines: c = sqrt(a² + b² - 2ab * cos(γ)). If you are working with angle-side-angle (ASA) or angle-angle-side (AAS) configurations, it applies the Law of Sines: a / sin(α) = b / sin(β) = c / sin(γ). Additionally, if the perimeter and two sides are provided, the missing third side is derived simply by subtracting the known lengths from the total perimeter value (c = Perimeter - a - b).

Imagine you are given a triangle where two interior angles are both 60° and one of the connecting sides measures 10 cm. Let us calculate the remaining side lengths step by step. First, because the sum of all angles in any triangle is always 180°, the third angle must also be 180° - 60° - 60° = 60°. Because all three angles are equal to 60°, we are dealing with an equilateral triangle. Using the Law of Sines, the ratio of any side to the sine of its opposite angle is constant. Thus, a = sin(60°) * 10 / sin(60°), which simplifies to 10 cm for all sides. Consequently, all three sides of this triangle measure exactly 10 cm.

To ensure maximum accuracy when finding triangle dimensions, always double-check your angle mode settings (degrees versus radians) before entering data. When using trigonometric formulas, be mindful of the triangle inequality theorem, which states that the sum of any two side lengths must always be strictly greater than the length of the remaining side. If your input numbers violate this rule, a valid geometric triangle cannot be formed.