1. What is the Law of Cosines?

The Law of Cosines is a formula relating 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.

2. How Does the Calculator Work?

The calculator uses the Law of Cosines formula:

Where:

• \( b \) — Length of side b
• \( c \) — Length of side c
• \( A \) — Angle between sides b and c (in degrees)

Explanation: The formula calculates the length of the side opposite angle A when you know the lengths of the other two sides and the included angle.

3. Importance of Triangle Side Calculation

Details: Calculating unknown sides of triangles is essential in geometry, trigonometry, navigation, engineering, and physics applications.

4. Using the Calculator

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

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) and need to find the third side.

Q2: 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.

Q3: Does the Law of Cosines work for right triangles?
A: Yes, and it simplifies to the Pythagorean theorem when the angle is 90° (since cos(90°) = 0).

Q4: What units should I use?
A: Any consistent units for length (meters, feet, etc.). The angle must always be in degrees.

Q5: Can I use this for obtuse triangles?
A: Yes, the Law of Cosines works for all triangle types (acute, right, and obtuse).