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'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 Law of Cosines formula:

Where:

• \( a \) — Length of side a (meters)
• \( b \) — Length of side b (meters)
• \( C \) — Angle between sides a and b (degrees)
• \( c \) — Length of the side opposite angle C (result)

Explanation: The formula calculates the length of the third side of a triangle when you know two sides and the included angle.

3. Importance of Triangle Side Calculation

Details: Calculating unknown sides of triangles is fundamental in geometry, navigation, engineering, and physics. The Law of Cosines is particularly useful in surveying, astronomy, and vector calculations.

4. Using the Calculator

Tips: Enter lengths of two sides and the included angle in degrees. All values must be positive, and the angle must be between 0 and 180 degrees.

5. Frequently Asked Questions (FAQ)

Q1: When should I use the Law of Cosines?
A: Use it when you know two sides of a triangle and the included angle (SAS), or when you know all three sides (SSS) and need to find an angle.

Q2: How is this different from the Pythagorean theorem?
A: The Pythagorean theorem only works for right triangles (c² = a² + b²). The Law of Cosines works for any triangle and reduces to the Pythagorean theorem when C = 90°.

Q3: What units should I use?
A: The calculator uses meters, but any consistent unit can be used as long as all lengths are in the same unit.

Q4: What if my angle is exactly 0° or 180°?
A: The triangle becomes degenerate (a straight line). The calculator only accepts angles between 0° and 180° exclusive.

Q5: Can I use this for navigation problems?
A: Yes, the Law of Cosines is commonly used in navigation to find distances between points when angles are known.