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's a generalization of the Pythagorean theorem that works 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 unknown side opposite angle C

Explanation: The formula calculates the length of the third side when two sides and the included angle are known.

3. Importance of Triangle Side Calculation

Details: Calculating unknown sides of triangles is fundamental in geometry, trigonometry, navigation, physics, engineering, and computer graphics.

4. Using the Calculator

Tips: Enter 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: Can this calculator work for any triangle?
A: Yes, the Law of Cosines works for all triangles - acute, right, and obtuse.

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: How accurate are the results?
A: Results are accurate to two decimal places. For exact values, symbolic computation may be needed.

Q4: Does the order of sides a and b matter?
A: No, the formula is symmetric with respect to sides a and b.

Q5: What about very small or very large angles?
A: The formula works for all angles between 0° and 180° (non-inclusive).