1. What is the Law of Cosines?

The Law of Cosines relates the lengths of the sides of a triangle to the cosine of one of its angles. It's particularly useful for solving scalene triangles where all sides have different lengths.

2. How Does the Calculator Work?

The calculator uses the Law of Cosines formula:

Where:

• \( a, b, c \) — Lengths of the sides of the triangle
• \( C \) — Angle opposite side c

Explanation: The formula calculates the cosine of angle C using the three side lengths, then uses the inverse cosine function to find the angle itself.

3. Importance of Angle Calculation

Details: Calculating angles in a scalene triangle is essential for various applications in geometry, trigonometry, navigation, engineering, and physics where precise angle measurements are needed.

4. Using the Calculator

Tips: Enter all three side lengths in the same units. The calculator will determine all three angles in either degrees or radians based on your selection.

5. Frequently Asked Questions (FAQ)

Q1: What is a scalene triangle?
A: A scalene triangle is a triangle where all three sides have different lengths and all three angles have different measures.

Q2: Can this calculator work for right triangles?
A: Yes, but for right triangles, using the Pythagorean theorem and basic trigonometric functions might be simpler.

Q3: What if my sides don't form a valid triangle?
A: The calculator checks for the triangle inequality theorem (sum of any two sides must be greater than the third side). Invalid inputs will not produce results.

Q4: How precise are the calculations?
A: The calculator provides results rounded to 2 decimal places, which is sufficient for most practical applications.

Q5: Can I use this for 3D triangles?
A: No, this calculator is designed for planar (2D) triangles only.