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 angle A
• \( b \) — Length of another side
• \( c \) — Length of the third side
• \( A \) — Angle opposite side a

Explanation: The formula calculates the angle opposite side 'a' when all three sides of the triangle are known.

3. Importance of Triangle Calculations

Details: Accurate triangle calculations are essential in geometry, trigonometry, navigation, engineering, and computer graphics for determining unknown angles or sides.

4. Using the Calculator

Tips: Enter all three side lengths in the same units. Values must be positive and must satisfy the triangle inequality theorem (sum of any two sides must be greater than the third).

5. Frequently Asked Questions (FAQ)

Q1: What if my sides don't form a valid triangle?
A: The calculator will show an error message if the side lengths violate the triangle inequality theorem.

Q2: Can I calculate sides if I know angles?
A: This calculator specifically calculates angles from sides. For side calculations, you would need a different implementation.

Q3: What units should I use?
A: Any consistent units can be used (cm, m, inches, etc.) as long as all three sides are in the same units.

Q4: How precise are the results?
A: Results are calculated to high precision and displayed with 2 decimal places.

Q5: Can this calculate all angles of a triangle?
A: This calculates one angle (opposite side 'a'). To find other angles, you would need to rearrange the formula with different sides.