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 for any triangle, not just right-angled ones.

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 when you know two sides and the included angle.

3. Importance of the Law of Cosines

Details: This law is essential in trigonometry for solving triangles when you have SAS (Side-Angle-Side) information. It's used in navigation, physics, engineering, and computer graphics.

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 and 180 degrees).

5. Frequently Asked Questions (FAQ)

Q1: Can this be used for right triangles?
A: Yes, when C=90°, the formula reduces to the Pythagorean theorem since cos(90°)=0.

Q2: What if I know three sides and need an angle?
A: The formula can be rearranged to solve for angles: \( \cos(C) = (a^2 + b^2 - c^2)/(2ab) \).

Q3: Does the order of sides a and b matter?
A: No, the formula is symmetric with respect to a and b.

Q4: What units should I use?
A: Any consistent length units (meters, feet, etc.) as long as all sides use the same unit.

Q5: Can this handle obtuse angles?
A: Yes, the formula works for all angles between 0° and 180°.