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, especially useful for scalene triangles where all sides have different lengths.

2. How Does the Calculator Work?

The calculator uses the Law of Cosines:

Where:

• \( a \) — Length of side a
• \( b \) — Length of side b
• \( c \) — Length of side c
• \( C \) — Angle opposite side c

Explanation: The equation calculates the cosine of angle C, which is then converted to degrees using the inverse cosine function.

3. Importance of Triangle Calculations

Details: Understanding triangle properties is fundamental in geometry, physics, engineering, and navigation. The Law of Cosines is particularly useful when dealing with non-right triangles.

4. Using the Calculator

Tips: Enter all three side lengths in the same units. The calculator will determine the angle opposite the third side (C). All side lengths must be positive numbers that satisfy the triangle inequality theorem.

5. Frequently Asked Questions (FAQ)

Q1: What is a scalene triangle?
A: A scalene triangle has all sides of different lengths and all angles of different measures.

Q2: What units should I use?
A: Any consistent length unit can be used (cm, m, inches, etc.), just ensure all sides use the same unit.

Q3: What if I get an error or invalid result?
A: Check that your side lengths satisfy the triangle inequality (sum of any two sides must be greater than the third).

Q4: Can I calculate other angles with this?
A: Yes, by rearranging the formula to solve for different angles using different side combinations.

Q5: How accurate are the results?
A: Results are accurate to two decimal places, sufficient for most practical applications.