1. What is the Scalene Triangle Angle Formula?

Definition: This calculator computes an angle in a scalene triangle (where all sides are of different lengths) using the Law of Cosines.

Purpose: It helps in geometry calculations when you know all three sides of a triangle and need to find one of its angles.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( C \) — Angle opposite to side c (degrees)
• \( a, b, c \) — Lengths of the triangle sides (meters)

Explanation: The formula is derived 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: Calculating angles in triangles is fundamental in geometry, trigonometry, and various practical applications like construction, navigation, and engineering.

4. Using the Calculator

Tips: Enter the lengths of all three sides in meters. The calculator will return angle C (the angle opposite side c) in degrees. All side lengths must be positive and must satisfy the triangle inequality theorem.

5. Frequently Asked Questions (FAQ)

Q1: What is a scalene triangle?
A: A scalene triangle is a triangle where all three sides have different lengths, and consequently all three angles are different.

Q2: Can this formula be used for any triangle?
A: Yes, the Law of Cosines works for all types of triangles, including equilateral and isosceles triangles.

Q3: What if I get an error or no result?
A: This typically means the side lengths don't form a valid triangle (violating the triangle inequality theorem) or there's a mathematical domain error in the arccos calculation.

Q4: How can I find the other angles?
A: After finding angle C, you can use the Law of Sines to find the other angles or use the Law of Cosines again with the sides rearranged.

Q5: What units should I use?
A: The calculator uses meters for side lengths, but any consistent unit can be used as long as all sides are in the same unit.