1. What is a Triangle Angle Calculator?

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

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

2. How Does the Calculator Work?

The calculator uses the Law of Cosines formula:

Where:

• \( C \) — Angle opposite side c (degrees)
• \( a, b, c \) — Lengths of the triangle sides (must satisfy triangle inequality)

Explanation: The formula relates the lengths of the sides of a triangle to the cosine of one of its angles.

3. Importance of Triangle Angle Calculation

Details: Accurate angle calculation is essential for proper construction, navigation, and various engineering applications.

4. Using the Calculator

Tips: Enter all three side lengths in the same units (default meters). The sides must satisfy the triangle inequality (sum of any two sides > third side).

5. Frequently Asked Questions (FAQ)

Q1: What if I get an "Invalid triangle" error?
A: This means your side lengths cannot form a triangle. Check that the sum of any two sides is 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: Which angle does this calculate?
A: It calculates angle C, which is opposite side c. For other angles, rearrange the formula.

Q4: How accurate is the calculation?
A: The calculation is mathematically precise, though real-world measurements may have practical limitations.

Q5: What about right triangles?
A: For right triangles (where c is hypotenuse), the formula simplifies to the Pythagorean theorem.