1. What is the Cosine Rule?

The Cosine Rule (also known as the Law of Cosines) relates the lengths of the sides of a triangle to the cosine of one of its angles. It's particularly useful for finding a missing side when you know two sides and the included angle.

2. How Does the Calculator Work?

The calculator uses the Cosine Rule:

Where:

• \( a \) — Length of side a
• \( b \) — Length of side b
• \( C \) — Angle between sides a and b (in degrees)
• \( c \) — Length of the missing side opposite angle C

Explanation: The rule calculates the third side of a triangle when two sides and the included angle are known.

3. Importance of the Cosine Rule

Details: The Cosine Rule is essential in trigonometry and geometry for solving triangles, particularly in cases where the triangle is not right-angled.

4. Using the Calculator

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

5. Frequently Asked Questions (FAQ)

Q1: When should I use the Cosine Rule?
A: Use it when you know two sides and the included angle (SAS) and need to find the third side.

Q2: How is this different from the Pythagorean theorem?
A: The Pythagorean theorem only works for right-angled triangles, while the Cosine Rule works for any triangle.

Q3: What units should I use?
A: Any consistent units can be used for side lengths, as long as both sides are in the same units.

Q4: What if my angle is exactly 90 degrees?
A: The Cosine Rule simplifies to the Pythagorean theorem when C = 90° (since cos(90°) = 0).

Q5: Can I use this to find an angle?
A: Yes, but this calculator is specifically for finding the missing side. The rearranged formula for angles is: \( \cos C = \frac{a^2 + b^2 - c^2}{2ab} \).