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 all 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 radians)
• \( c \) — Length of the side opposite angle C

Explanation: The rule is a generalization of the Pythagorean theorem that works for any triangle, not just right-angled ones.

3. Importance of the Cosine Rule

Details: The Cosine Rule is fundamental in trigonometry and has applications in navigation, physics, engineering, and computer graphics. It's essential for solving oblique triangles.

4. Using the Calculator

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

5. Frequently Asked Questions (FAQ)

Q1: Can I use degrees instead of radians?
A: This calculator uses radians. To convert degrees to radians, multiply by π/180 (approximately 0.0174533).

Q2: What if I know all three sides but no angles?
A: You can rearrange the formula to solve for an angle: \( \cos(C) = \frac{a^2 + b^2 - c^2}{2ab} \)

Q3: How accurate is the calculation?
A: The calculator provides results with 4 decimal places, but precision depends on your input values.

Q4: Does this work for any triangle?
A: Yes, the Cosine Rule applies to all triangles, whether acute, right, or obtuse.

Q5: What's the relationship with the Pythagorean theorem?
A: For right-angled triangles (C = π/2 radians), cos(C) = 0 and the formula reduces to the Pythagorean theorem.