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 generalizes the Pythagorean theorem and works for any type of triangle, not just right-angled ones.

2. How Does the Calculator Work?

The calculator uses the Law of Cosines formula:

Where:

• \( a \) — Length of side opposite the angle you're calculating
• \( b \) — Length of another side
• \( c \) — Length of the remaining side

Explanation: The formula calculates the angle opposite side 'a' by using the relationship between all three sides of the triangle.

3. Importance of Angle Calculation

Details: Calculating angles in triangles is fundamental in geometry, trigonometry, navigation, engineering, and computer graphics. It helps in determining the shape and dimensions of triangles when all sides are known.

4. Using the Calculator

Tips: Enter the lengths of all three sides of the triangle. Side 'a' should be the side opposite the angle you want to calculate. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What if the sides don't form a valid triangle?
A: The calculator will return an error or undefined result if the side lengths violate the triangle inequality theorem (sum of any two sides must be greater than the third).

Q2: Can I calculate other angles with this?
A: Yes, just rotate which side you call 'a' to calculate different angles. You'll need to run the calculation separately for each angle.

Q3: What units should I use?
A: Any consistent units (cm, inches, etc.) as long as all three sides use the same unit.

Q4: How accurate is the calculation?
A: The calculation is mathematically precise, though real-world measurements will have their own accuracy limitations.

Q5: What if I only know two sides and an included angle?
A: Use the Law of Cosines in reverse to find the third side first, then you can calculate other angles.