📚 Law of Cosines Calculator

🎯 What is the Law of Cosines?

The Law of Cosines is like the Pythagorean theorem’s big brother – it works for ALL triangles, not just right triangles! It helps you find missing sides or angles when you have partial triangle information.

🔍 When Do You Use It?

Scenario 1: Find a Missing Side

• You know two sides and the angle between them (SAS)
• Example: Side A = 5, Side B = 7, Angle C = 60°
• Goal: Find Side C

Scenario 2: Find a Missing Angle

• You know all three sides (SSS)
• Example: Side A = 3, Side B = 4, Side C = 5
• Goal: Find any angle

🎮 How to Use the Calculator

Step 1: Choose What to Calculate

1. Click the blue dropdown that says “Side A”
2. Select what you want to find:
   • Side A, B, or C (if you need a missing side)
   • Angle A, B, or C (if you need a missing angle)

Step 2: Enter Your Known Values

• Fill in the input boxes with the numbers you know
• Leave empty the value you’re trying to find
• The calculator is smart – it knows what you need!

Step 3: Set Your Preferences

• Angle Units: Degrees (easier) or Radians (advanced)
• Length Units: Choose meters, feet, inches, etc.
• Decimal Places: How precise you want your answer

Step 4: Hit Calculate!

Click the big orange “Calculate Triangle” button 🧮

📊 Understanding Your Results

The Answer Box (Green)

• Shows your final answer in big, bold text
• Includes the correct units (degrees for angles, your chosen unit for sides)

Step-by-Step Solution

• See exactly how the calculator solved the problem
• Follow along with the formula substitution
• Perfect for checking your homework!

Visual Triangle

• Watch your triangle come to life on the right side
• See all sides labeled with their lengths
• Angles are marked with their degree measurements
• Colors help you identify different parts

🎨 Cool Visual Features

Interactive Triangle Drawing

• Real-time updates as you enter data
• Proportional sizing – bigger sides look bigger!
• Color-coded labels for easy identification

Angle Distribution Chart

• Progress bars show how big each angle is
• Helps you visualize if your triangle makes sense
• All angles should add up to 180°

Formula Display

• Shows the exact formula being used
• Updates automatically based on what you’re calculating
• Great for learning the math behind it

🚀 Bonus Features for Extra Credit

📐 Area Button

• Calculates triangle area using your sides/angles
• Shows two different methods (SAS formula or Heron’s formula)
• Great for geometry projects

📏 Perimeter Button

• Adds up all three sides instantly
• Perfect for real-world applications

🔄 All Angles Button

• If you have all sides, this finds all three angles
• Super helpful for checking triangle validity

📊 All Sides Button

• Shows complete triangle information
• Great summary view of your triangle

💡 Study Tips

Common Student Mistakes to Avoid:

1. Wrong angle units – Make sure you’re using degrees or radians consistently
2. Impossible triangles – If you get an error, check that your sides can actually form a triangle
3. Angle confusion – Remember: Angle A is opposite Side A, etc.

Practice Strategy:

1. Start simple – Use nice round numbers first
2. Check your work – All angles should add to 180°
3. Use the visual – Does your triangle look right?
4. Try the reverse – Calculate a side, then use it to find an angle

Real-World Applications:

• Construction projects (roof angles, building layouts)
• Navigation (GPS and mapping)
• Engineering (bridge design, structural analysis)
• Art and design (creating geometric patterns)

🎯 Quick Reference

For Finding Sides:

Need: Two sides + included angle
Formula: c² = a² + b² - 2ab×cos(C)

For Finding Angles:

Need: All three sides
Formula: cos(A) = (b² + c² - a²) ÷ (2bc)

🏆 Pro Tips

• Save your work by taking screenshots of results
• Experiment with different triangles to see patterns
• Use the clear button to start fresh problems
• Mobile friendly – works great on phones for homework on-the-go!

This calculator turns the sometimes-intimidating Law of Cosines into an interactive, visual learning experience. It’s like having a math tutor that never gets tired of explaining the same concept! 📚✨