1. What is the SSS Triangle Angle Formula?

The SSS (Side-Side-Side) triangle angle formula calculates an angle when all three sides of a triangle are known. It's derived from the Law of Cosines and provides accurate angle measurements for any valid triangle.

2. How Does the Calculator Work?

The calculator uses the SSS angle formula:

Where:

• \( a, b, c \) — Lengths of the triangle sides
• \( A \) — Angle opposite to side \( a \)
• \( \arccos \) — Inverse cosine function

Explanation: The formula calculates angle A using the relationship between all three sides of the triangle and the cosine rule.

3. Importance of Triangle Angle Calculation

Details: Calculating angles from sides is essential in trigonometry, engineering, architecture, and navigation. It helps determine the complete shape of a triangle when only side lengths are known.

4. Using the Calculator

Tips: Enter all three side lengths in the same units. The calculator will verify if the sides can form a valid triangle (satisfying the triangle inequality theorem) before computing the angle.

5. Frequently Asked Questions (FAQ)

Q1: What is the triangle inequality theorem?
A: It states that the sum of any two sides must be greater than the third side for a valid triangle.

Q2: Can I calculate other angles with this formula?
A: Yes, by rotating which side is considered 'a' in the formula, you can calculate all three angles.

Q3: What's the difference between degrees and radians?
A: Degrees range 0-360 for a full circle, while radians range 0-2π. 1 radian ≈ 57.2958 degrees.

Q4: What if I get an error message?
A: Check that your side lengths satisfy the triangle inequality (sum of any two sides > third side).

Q5: How precise are the calculations?
A: The calculator provides results with 2 decimal places for degrees and 4 for radians.