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:

• \( a \) — 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 of a triangle when you know two sides and the included angle.

3. Importance of the Law of Cosines

Details: This law is essential in trigonometry and geometry for solving triangles, especially when the triangle is not right-angled. It's used in navigation, physics, engineering, and computer graphics.

4. Using the Calculator

Tips: Enter lengths of sides a and b in any consistent units, and the included angle C in degrees. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

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

Q2: What units should I use?
A: Any consistent length units (cm, m, inches, etc.). The result will be in the same units as your input.

Q3: What's the range for angle C?
A: The angle must be between 0° and 180° for a valid triangle.

Q4: Can I find angles with this formula?
A: Yes, the formula can be rearranged to find angles when all three sides are known.

Q5: How accurate are the results?
A: The calculator provides results rounded to 2 decimal places, but exact accuracy depends on your input values.