1. What is the Law of Cosines Calculator?

Definition: This calculator solves for the third side of a triangle when two sides and the included angle are known, using the Law of Cosines formula.

Purpose: It helps in trigonometry and geometry problems, particularly in non-right-angled triangles.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( a \) — Length of side a (meters)
• \( b \) — Length of side b (meters)
• \( C \) — Included angle between sides a and b (degrees)
• \( c \) — Length of the calculated side (meters)

Explanation: The formula relates the lengths of the sides of a triangle to the cosine of one of its angles.

3. Importance of the Law of Cosines

Details: The Law of Cosines is essential for solving triangles when the SAS (Side-Angle-Side) information is known, extending beyond right-angled triangles.

4. Using the Calculator

Tips: Enter the lengths of sides a and b (must be positive), and the included angle C (must be between 0° and 180°).

5. Frequently Asked Questions (FAQ)

Q1: When should I use the Law of Cosines?
A: Use it when you know two sides and the included angle (SAS) of a triangle and need to find the third side.

Q2: How does this differ from the Pythagorean theorem?
A: The Pythagorean theorem only works for right-angled triangles, while the Law of Cosines works for any triangle.

Q3: What units should I use?
A: Any consistent units can be used (meters, feet, etc.), but all sides must use the same unit.

Q4: What if my angle is exactly 90 degrees?
A: The Law of Cosines reduces to the Pythagorean theorem when C = 90° (since cos(90°) = 0).

Q5: Can I find angles with this formula?
A: Yes, but this calculator focuses on finding the third side. The formula can be rearranged to find angles when all three sides are known.