1. What is a Triangle Angle Calculator?

Definition: This calculator computes an angle of a triangle when all three side lengths are known, using the Law of Cosines.

Purpose: It helps in geometry, trigonometry, and various engineering applications where triangle measurements are needed.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( C \) — Angle opposite side c (degrees)
• \( a \) — Length of side a (meters)
• \( b \) — Length of side b (meters)
• \( c \) — Length of side c (meters)

Explanation: The formula derives from the Law of Cosines, which relates the lengths of the sides of a triangle to the cosine of one of its angles.

3. Importance of Angle Calculation

Details: Accurate angle calculation is essential in construction, navigation, computer graphics, and any field requiring precise geometric measurements.

4. Using the Calculator

Tips: Enter all three side lengths in the same units (default meters). All values must be positive and satisfy the triangle inequality theorem.

5. Frequently Asked Questions (FAQ)

Q1: What if I get "NaN" as a result?
A: This means the input values don't form a valid triangle. The sum of any two sides must be greater than the third side.

Q2: Can I use different units?
A: Yes, as long as all three sides use the same unit (e.g., all in feet or all in meters).

Q3: How accurate is the calculation?
A: The calculation is mathematically precise, though displayed results are rounded to 2 decimal places.

Q4: Can I calculate other angles with this?
A: Yes, just rotate which side is "c" to calculate different angles. For angle A, make side a opposite, etc.

Q5: What about right triangles?
A: For right triangles, when c is the hypotenuse, the formula simplifies to arccos(0) = 90° as expected.