Law of Cosines Calculator
Calculate triangle sides and angles using the cosine rule formula
Triangle Parameters
Triangle Sides
Triangle Angles
Calculation Results
Triangle Properties
Quick Examples
When to Use Law of Cosines Calculator
Engineering Design
Calculate structural angles and distances in construction, mechanical design, and architectural planning where precise measurements are critical.
Navigation & GPS
Determine distances and bearings in navigation systems, surveying, and GPS applications where triangulation is essential.
Physics Problems
Solve vector problems, force analysis, and motion calculations in physics where triangular relationships define system behavior.
Game Development
Calculate collision detection, pathfinding algorithms, and 3D graphics transformations in game engines and interactive applications.
Academic Learning
Study trigonometry, geometry, and advanced mathematics concepts with step-by-step solutions and formula explanations.
Land Surveying
Measure property boundaries, topographical features, and create accurate maps using triangulation methods and precise angle calculations.
Frequently Asked Questions
What is the law of cosines?
The law of cosines is a fundamental trigonometric formula that relates the lengths of the sides of a triangle to the cosine of one of its angles. It states: c² = a² + b² - 2ab cos(C), where c is the side opposite angle C. This formula extends the Pythagorean theorem to work with any triangle, not just right triangles.
When should I use the law of cosines?
Use the law of cosines when you know three sides of a triangle (SSS case) and need to find an angle, or when you know two sides and the included angle (SAS case) and need to find the third side. It's particularly useful when the law of sines cannot be applied or when you need more precise calculations.
How is this different from the law of sines?
The law of cosines is used for SSS and SAS triangle cases, while the law of sines is used for ASA, AAS, and SSA cases. The law of cosines involves squared terms and cosine functions, making it more suitable for certain geometric problems. Both laws are complementary tools in triangle solving.
Can this calculator solve any triangle?
This calculator can solve triangles when you have sufficient information: three sides (SSS), two sides and the included angle (SAS), or when combined with other triangle properties. It cannot solve triangles with insufficient data or invalid triangle configurations that violate the triangle inequality theorem.
What units does the calculator support?
The calculator supports both degrees and radians for angles, and any consistent length units for sides (meters, feet, inches, centimeters, etc.). Results maintain the same units as your input. The key is to use consistent units throughout your calculation.
Is this law of cosines calculator free?
Yes, our law of cosines calculator is completely free to use. There are no limits on calculations, no registration required, and all features including step-by-step solutions, formula explanations, and result downloads are available at no cost.
How accurate are the calculations?
The calculator uses high-precision mathematical functions and provides results accurate to the decimal places you specify (2-6 places). All calculations follow standard mathematical principles and include validation to ensure triangle validity and mathematical correctness.
No comments yet. Be the first to share your thoughts!