How to Use the Law of Sines and Cosines Calculator
The Law of Sines and Cosines Calculator solves a triangle when you only know some of its sides and angles. Choose the input type that matches what you know — three sides (SSS), two sides and the included angle (SAS), or two angles and a side (ASA) — and the calculator automatically applies the right formula. SSS and SAS use the law of cosines (a² = b² + c² - 2bc·cosA), while ASA uses the law of sines (a/sinA = b/sinB = c/sinC) to find the remaining angles and sides.
After selecting the input type and entering the known values, all three angles and sides appear instantly in a table. If the three side lengths don't satisfy the triangle inequality (each side must be shorter than the sum of the other two), or if the included angle or angle sum falls outside a valid range, an error message explains why. This is especially useful in surveying, construction, and navigation, where only some measurements are available.
Frequently Asked Questions
Use the law of sines when you know two angles and a side (ASA). Use the law of cosines when you know three sides (SSS) or two sides and the included angle (SAS). This calculator applies the right formula automatically based on the input type you choose.
A triangle can only exist if each side is shorter than the sum of the other two. Check whether your three lengths satisfy this triangle inequality.
All angles are entered in degrees. For example, for 60 degrees, just enter 60.