Triangle Length Calculator

This calculator relies on foundational trigonometric laws, primarily the Law of Cosines and the Triangle Angle Sum Theorem. The Law of Cosines states that for any triangle with sides a, b, and c and corresponding opposite angles A, B, and C, the relationship is defined as c² = a² + b² - 2ab * cos(C). Additionally, the internal angles of any triangle always sum up to exactly 180 degrees (or pi radians), meaning angle A equals pi minus the sum of angle B and angle C.

Imagine you have a triangle where side 'a' is 10 units long, angle A is 60 degrees, and angle B is 45 degrees. First, find the third angle (angle C) by subtracting the known angles from 180 degrees: C = 180° - (60° + 45°) = 75°. Next, apply the Law of Sines or Law of Cosines to solve for the unknown side lengths 'b' and 'c'. Using the proportional relationship of the Law of Sines (a / sin(A) = b / sin(B)), we calculate side 'b' as (10 * sin(45°)) / sin(60°), which yields approximately 8.16 units. Finally, solve for side 'c' using the same proportion, resulting in approximately 11.15 units.

Always ensure your calculator or input mode matches your preferred unit of measurement, switching correctly between degrees and radians before entering angle values. Double-check that your known inputs actually form a valid triangle; for instance, the sum of any two side lengths must always be strictly greater than the length of the remaining third side.