1. What is the Scalene Triangle Angle Formula?

The Law of Cosines relates the lengths of the sides of a triangle to the cosine of one of its angles. For angle A opposite side a, with sides b and c adjacent, the formula is:

2. How Does the Calculator Work?

The calculator uses the Law of Cosines to determine the angle opposite the specified side in a scalene triangle.

Steps:

1. Calculate the numerator: b² + c² - a²
2. Calculate the denominator: 2 × b × c
3. Divide numerator by denominator
4. Take the arccosine of the result
5. Convert to degrees if selected

3. Importance of Angle Calculation

Applications: Calculating angles in scalene triangles is essential in trigonometry, navigation, engineering, computer graphics, and physics problems involving vector analysis.

4. Using the Calculator

Instructions: Enter all three side lengths (must be positive numbers that satisfy the triangle inequality theorem). Select whether you want the result in degrees or radians.

5. Frequently Asked Questions (FAQ)

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

Q2: Why does my input result in "Invalid triangle sides"?
A: The sum of any two sides must be greater than the third side. If not, they cannot form a triangle.

Q3: Can I calculate other angles with this?
A: Yes, just rotate which side is considered "a" to calculate different angles.

Q4: What's the difference between degrees and radians?
A: Degrees divide a circle into 360 units, while radians use 2π (about 6.283) units. Radians are often preferred in higher mathematics.

Q5: How accurate is this calculation?
A: The calculation is mathematically precise, though displayed results are rounded for readability.