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 to any triangle, not just right-angled ones.

2. How Does the Calculator Work?

The calculator uses the Law of Cosines formula:

Where:

• \( a, b, c \) — Sides of the triangle (meters)
• \( C \) — Angle opposite side c (degrees)

Explanation: The formula can be rearranged to solve for any side or angle when you know the other three values.

3. When to Use the Law of Cosines

Details: Use this law when you know:

• Two sides and the included angle (to find the third side)
• Three sides (to find any angle)

4. Using the Calculator

Tips: Enter any three values (two sides and one angle or three sides) and leave one field blank to calculate the missing value.

5. Frequently Asked Questions (FAQ)

Q1: When should I use Law of Cosines vs Law of Sines?
A: Use Law of Cosines when you have SAS (side-angle-side) or SSS (side-side-side) information. Use Law of Sines for ASA or AAS cases.

Q2: Can this be used for right triangles?
A: Yes, but the Pythagorean theorem is simpler for right triangles (when C=90°, cos(C)=0).

Q3: What units should I use?
A: Use consistent units for all sides. Angles must be in degrees.

Q4: What if I get an error?
A: Check that the values satisfy the triangle inequality theorem (sum of any two sides > third side).

Q5: Can I calculate multiple values at once?
A: No, the calculator solves for one missing value at a time given three known values.