1. What is the Law of Cosines Calculator?

Definition: This calculator computes the length of a side of a triangle when you know the lengths of the other two sides and the included angle.

Purpose: It helps in solving triangles in trigonometry, navigation, engineering, and physics problems.

2. How Does the Calculator Work?

The calculator uses the Law of Cosines formula:

Where:

• \( a \) — Length of side opposite angle A (meters)
• \( b \) — Length of one adjacent side (meters)
• \( c \) — Length of the other adjacent side (meters)
• \( A \) — Included angle between sides b and c (degrees)

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

3. Importance of Triangle Calculations

Details: Accurate triangle calculations are essential in construction, navigation, astronomy, and various engineering fields.

4. Using the Calculator

Tips: Enter the lengths of sides b and c in meters, and the included angle A in degrees (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) or all three sides (SSS) of a triangle.

Q2: What's the difference between Law of Cosines and Law of Sines?
A: Law of Sines relates sides to opposite angles, while Law of Cosines relates all three sides to one angle.

Q3: Can the angle be 90 degrees?
A: Yes, and when it is, the formula simplifies to the Pythagorean theorem since cos(90°) = 0.

Q4: What units should I use?
A: The calculator uses meters, but any consistent unit will work as long as all sides use the same unit.

Q5: What if I get an error or imaginary result?
A: This means the given sides and angle cannot form a valid triangle. Check your inputs.