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:

• An angle when you know all three sides of a triangle
• The third side when you know two sides and the included angle

2. How Does the Calculator Work?

The calculator uses the cosine rule formula:

Where:

• \( a \) and \( b \) — Lengths of the sides adjacent to angle θ
• \( c \) — Length of the side opposite angle θ
• \( \theta \) — The angle you're calculating (in degrees)

Explanation: The formula calculates the cosine of angle θ using the side lengths, then takes the inverse cosine (arccos) to find the angle in radians, which is then converted to degrees.

3. When to Use the Cosine Rule

Details: The cosine rule is most useful when:

• You know all three sides of a triangle (SSS)
• You know two sides and the included angle (SAS)

For right-angled triangles, the Pythagorean theorem is simpler.

4. Using the Calculator

Tips:

• Enter all three side lengths in the same units
• Side c must be opposite the angle you're calculating
• Values must satisfy the triangle inequality (sum of any two sides > third side)

5. Frequently Asked Questions (FAQ)

Q1: What if I get an error message about invalid triangle?
A: This means your side lengths don't satisfy the triangle inequality theorem. Check your measurements.

Q2: How accurate is this calculation?
A: The calculation is mathematically exact (given precise inputs). Rounding occurs only in the final display.

Q3: Can I use this for any triangle?
A: Yes, the cosine rule works for all triangles - acute, right, and obtuse.

Q4: What units should I use?
A: Any consistent units (cm, m, inches, etc.), but all sides must be in the same units.

Q5: Can I find a side length instead of an angle?
A: Yes, the cosine rule can be rearranged to find side c: \( c = \sqrt{a^2 + b^2 - 2ab\cos(\theta)} \)