1. What is the Law of Cosines?

The Law of Cosines is a fundamental trigonometric formula that relates the lengths of the sides of a triangle to the cosine of one of its angles. It is particularly useful for solving triangles when you know all three sides or two sides and the included angle.

2. How Does the Calculator Work?

The calculator uses the Law of Cosines formula:

Where:

• \( a \) — Side opposite angle A
• \( b \) — Adjacent side
• \( c \) — Adjacent side
• \( \arccos \) — Inverse cosine function

Explanation: The formula calculates angle A using the lengths of all three sides of the triangle, where side a is opposite the angle being calculated.

3. Importance of Angle Calculation

Details: Accurate angle calculation is crucial for geometry problems, engineering applications, navigation, computer graphics, and various scientific calculations involving triangles.

4. Using the Calculator

Tips: Enter all three side lengths in the same units. All values must be positive numbers that satisfy the triangle inequality theorem (sum of any two sides must be greater than the third side).

5. Frequently Asked Questions (FAQ)

Q1: What units should I use for the side lengths?
A: You can use any consistent units (cm, inches, meters, etc.) as long as all three sides are in the same units.

Q2: Why does the calculator sometimes show "Invalid triangle sides"?
A: This occurs when the entered side lengths cannot form a valid triangle according to the triangle inequality theorem.

Q3: Can I calculate other angles with this formula?
A: Yes, you can calculate any angle by rearranging the formula to make the desired angle the subject.

Q4: How accurate is the calculation?
A: The calculation is mathematically precise, limited only by the precision of your input values and computer floating-point arithmetic.

Q5: What if I need to calculate in radians instead of degrees?
A: The calculator outputs degrees. If you need radians, you can convert using the formula: radians = degrees × π/180.