Law of Cosines Calculator

Law of Cosines Calculator: Comprehensive Guide

What Is It?

The Law of Cosines Calculator solves any triangle when you know:

• Two sides and their included angle (SAS)
• Three sides (SSS)
  It automatically calculates:
• Missing side lengths
• All angle measurements
• Triangle perimeter and area
• Visual representation

Key Formulas

1. Standard Form: $$c² = a² + b² - 2ab·cos(C)$$
2. Angle Calculation: $$cos(C) = (a² + b² - c²)/(2ab)$$
3. Variations:
   • For side b: b² = a² + c² - 2ac·cos(B)
   • For side a: a² = b² + c² - 2bc·cos(A)

How to Use

1. Select Calculation Mode:
   • SAS (Side-Angle-Side)
   • SSS (Side-Side-Side)
2. Enter Known Values:
   • For SAS: Two sides + included angle
   • For SSS: All three sides
3. View Results:
   • Complete triangle measurements
   • Graphical representation
   • Step-by-step solution
4. Advanced Features:
   • Unit conversion (degrees/radians)
   • Decimal precision adjustment
   • Calculation history

FAQs

Q: When should I use Law of Cosines vs Law of Sines?
A: Use Cosines for SAS/SSS cases, Sines for ASA/AAS cases. Cosines always works for any triangle type.

Q: How accurate are the calculations?
A: Results are precise to 12 decimal places, with visual verification.

Q: Can I calculate area with this tool?
A: Yes, it automatically computes area using Heron’s formula when three sides are known.

Terminology

• SAS: Side-Angle-Side configuration
• SSS: Side-Side-Side configuration
• Included Angle: The angle between two known sides
• Oblique Triangle: Any non-right triangle
• Scalene Triangle: Triangle with all sides/angles unequal
• Heron’s Formula: Area calculation using three sides

Practical Applications

1. Surveying and navigation
2. Engineering design
3. Computer graphics
4. Physics vector calculations
5. Architectural planning