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, including oblique triangles (non-right-angled triangles).

2. How Does the Calculator Work?

The calculator uses the Law of Cosines formula:

Where:

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

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 Oblique Triangle Calculations

Details: The Law of Cosines is essential in trigonometry and has applications in navigation, physics, engineering, and computer graphics where non-right-angled triangles are common.

4. Using the Calculator

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

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between Law of Cosines and Law of Sines?
A: Law of Cosines relates all three sides and one angle, while Law of Sines relates sides to their opposite angles. Use Law of Cosines when you have SAS (side-angle-side) or SSS (side-side-side) information.

Q2: Can this calculator find angles?
A: This version calculates the third side given two sides and the included angle. The formula can be rearranged to find angles if you know all three sides.

Q3: What units should I use?
A: Any consistent length units (meters, feet, etc.). The angle must be in degrees.

Q4: What if I get an error or imaginary number?
A: This would happen if the given sides and angle don't form a valid triangle (e.g., angle too large for given sides). Check your inputs.

Q5: Can this be used for right triangles?
A: Yes, but when C = 90°, cos(90°) = 0 and the formula reduces to the Pythagorean theorem.