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 solving triangles when you know two sides and the included angle, or three sides.

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 side opposite angle C

Explanation: The rule is derived from the Pythagorean theorem extended to non-right triangles. The term \( 2ab \cos C \) adjusts for the angle between sides a and b.

3. Importance of Triangle Calculations

Details: The Cosine Rule is essential in trigonometry, navigation, engineering, and physics for solving triangles when the Sine Rule cannot be applied. It's particularly useful in surveying and construction.

4. Using the Calculator

Tips: Enter lengths of sides a and b, and the included angle C in degrees. All values must be positive, and angle C must be between 0° and 180° (non-inclusive).

5. Frequently Asked Questions (FAQ)

Q1: When should I use the Cosine Rule vs. the Sine Rule?
A: Use the Cosine Rule when you know two sides and the included angle (SAS) or three sides (SSS). Use the Sine Rule when you know two angles and one side (AAS or ASA).

Q2: Does this work for right-angled triangles?
A: Yes, for a right angle (90°), the cosine term becomes zero and the formula reduces to the Pythagorean theorem.

Q3: What units should I use?
A: The units must be consistent for all sides. The angle must be in degrees.

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

Q5: What if I get an error or imaginary number?
A: This would happen if the given sides and angle cannot form a valid triangle (e.g., if the sum of two sides is less than the third). Check your inputs.