1. What is the Law of Cosines?

The Law of Cosines is a fundamental theorem in trigonometry 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 side lengths.

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 the angle opposite side a using the relationship between all three sides of the triangle.

3. Importance of Angle Calculation

Details: Calculating angles in triangles is essential in geometry, engineering, navigation, and various scientific applications. It helps determine unknown angles when side lengths are known.

4. Using the Calculator

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

5. Frequently Asked Questions (FAQ)

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

Q2: What units should I use for the side lengths?
A: You can use any consistent units (cm, m, inches, etc.) as long as all three sides use the same unit system.

Q3: Can I calculate other angles with this calculator?
A: This calculator specifically calculates angle A. To find other angles, you would need to rearrange the formula accordingly.

Q4: What if I get an error message?
A: The error indicates that the side lengths cannot form a valid triangle. Please check your input values.

Q5: How accurate is the calculation?
A: The calculation is mathematically precise based on the input values, with results rounded to two decimal places for clarity.