1. What is the Law of Cosines Calculator?

Definition: This calculator finds the missing side of a triangle when you know two sides and the included angle using the Law of Cosines.

Purpose: It helps solve oblique (non-right) triangles in mathematics, engineering, and various practical applications.

2. How Does the Calculator Work?

The calculator uses the Law of Cosines formula:

Where:

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

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 you don't have a right angle. It's used in navigation, construction, physics, and computer graphics.

4. Using the Calculator

Tips: Enter the lengths of two sides and the included angle (must be between 0° and 180°). All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: When should I use the Law of Cosines vs. Law of Sines?
A: Use Law of Cosines when you know two sides and the included angle (SAS) or all three sides (SSS). Use Law of Sines when you know two angles and one side (ASA or AAS).

Q2: What units should I use?
A: Any consistent units (meters, feet, etc.) for sides. Angle must be in degrees.

Q3: Why is there a limit on the angle size?
A: In a triangle, angles must be between 0° and 180° (exclusive) to form a valid triangle.

Q4: Can I find angles with this calculator?
A: This version calculates a missing side. For angles, you would need the version that rearranges the formula to solve for angles.

Q5: What if I get an error or imaginary number?
A: This indicates the inputs don't form a valid triangle. Check your measurements and ensure the angle is between the two given sides.