1. What is the Cosine Rule?

The cosine rule (law of cosines) relates the lengths of the sides of a triangle to the cosine of one of its angles. It's a generalization of the Pythagorean theorem that works for any triangle, not just right-angled ones.

2. How Does the Calculator Work?

The calculator uses the cosine rule formula:

Where:

• \( a \) — Length of side a
• \( b \) — Length of side b
• \( c \) — Length of side c (opposite to angle θ)
• \( \theta \) — Angle between sides a and b

Explanation: The formula calculates the angle opposite to side c in a triangle with sides a, b, and c.

3. Importance of Angle Calculation

Details: Calculating angles in triangles is fundamental in geometry, engineering, architecture, and navigation. It's essential for solving triangles when you know all three sides (SSS case).

4. Using the Calculator

Tips: Enter the lengths of all three sides of the triangle. The calculator will find the angle opposite to side c. All sides must be positive numbers and must satisfy the triangle inequality (sum of any two sides must be greater than the third).

5. Frequently Asked Questions (FAQ)

Q1: What units should I use for the sides?
A: Any consistent units can be used (cm, m, inches, etc.), as long as all three sides are in the same units.

Q2: Can this calculate all three angles of a triangle?
A: Yes, you can use the calculator three times, each time making a different side the "side c" (opposite to the angle you want to find).

Q3: What if I get an error message?
A: The error means your side lengths don't form a valid triangle. Check that the sum of any two sides is greater than the third side.

Q4: How accurate is the calculation?
A: The calculation is mathematically exact, though displayed results are rounded to 2 decimal places.

Q5: Can this be used for right-angled triangles?
A: Yes, it works for all triangles. For right-angled triangles, when c is the hypotenuse, the formula simplifies to θ = arccos(0) = 90°.