1. What is the Triangle Angle Calculator?

The Triangle Angle Calculator computes an angle of a triangle when all three side lengths are known, using the Law of Cosines. This is useful in geometry, trigonometry, and various practical applications.

2. How Does the Calculator Work?

The calculator uses the Law of Cosines formula:

Where:

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

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

3. Importance of Angle Calculation

Details: Calculating angles from sides is fundamental in trigonometry, navigation, engineering, and computer graphics. It helps solve triangles when only side lengths are known.

4. Using the Calculator

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

5. Frequently Asked Questions (FAQ)

Q1: What if my sides don't form a valid triangle?
A: The calculator will show an error message if the side lengths violate the triangle inequality theorem.

Q2: Can I calculate other angles with this?
A: Yes, you can calculate any angle by changing which side is opposite in the formula (rotate a, b, c accordingly).

Q3: What's more accurate - degrees or radians?
A: Radians are more mathematically precise, but degrees are more intuitive for most practical applications.

Q4: Does the order of sides matter?
A: Yes, the angle calculated is always opposite to the first side (a) in the formula.

Q5: Can this be used for any triangle?
A: Yes, it works for acute, right, and obtuse triangles as long as the sides form a valid triangle.