doomath Calculator
Trigonometry & Law of Sines/Cosines Solver
Solve triangles using the Law of Cosines and Law of Sines. Computes all 6 trigonometric ratios (sin, cos, tan, csc, sec, cot) and triangle area.
InputsChange a value to recalculate instantly
ResultUpdates as you type
FORMULA & STEPSTrigonometry & Law of Sines/Cosines Solver — Mathematical Derivation & Steps
3 StepsSequential Calculation Breakdown
1
Law of Cosines
Solve the side opposite the known included angle.
2
Remaining angles
Use the cosine rule and the 180° triangle angle sum.
3
Area
Use two sides and their included angle.
λ DooMathWork with this calculation
Local · deterministic · optionalQuick mathNatural-language-style shortcuts for deterministic arithmetic.
Calculator guide
How to use the Trigonometry & Law of Sines/Cosines Solver
Solve triangles using the Law of Cosines and Law of Sines. Computes all 6 trigonometric ratios (sin, cos, tan, csc, sec, cot) and triangle area.
01Set inputsChoose values, units and assumptions.
02Apply the modelc² = a² + b² - 2ab cos(C); a/sin(A) = b/sin(B) = c/sin(C); Area = ½ab sin(C)
03Read the resultCheck the output against the assumptions before using it.
What this calculator does
Input known side lengths and included angle C. The calculator applies the Law of Cosines to solve the third side, computes missing angles, and evaluates trigonometric functions.
Formula & method
c² = a² + b² - 2ab cos(C); a/sin(A) = b/sin(B) = c/sin(C); Area = ½ab sin(C)
Assumptions & notes
- The Law of Cosines generalizes the Pythagorean theorem to arbitrary triangles.
- The sum of internal angles in Euclidean space is always 180° (π radians).
- Heron's formula calculates triangle area purely from its three side lengths.