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 finding an angle when all three sides of a triangle are known.

2. How Does the Calculator Work?

The calculator uses the Law of Cosines formula:

Where:

• \( a \) — Side opposite to the angle being calculated
• \( b \) — One adjacent side
• \( c \) — The other adjacent side
• \( \arccos \) — Inverse cosine function

Explanation: The formula calculates the angle opposite to side a using the lengths of all three sides of the triangle.

3. Importance of Triangle Angle Calculation

Details: Calculating interior angles of triangles is essential in geometry, engineering, architecture, navigation, and various scientific applications where triangular relationships need to be determined.

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 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 are measured in the same units.

Q2: Why does the calculator show an error?
A: The error occurs when the entered side lengths cannot form a valid triangle according to the triangle inequality theorem.

Q3: Can I calculate angles for any type of triangle?
A: Yes, the Law of Cosines works for all types of triangles - acute, right, and obtuse.

Q4: What's the range of possible angle values?
A: Interior angles of a triangle range from >0° to <180°, and the sum of all three angles is always 180°.

Q5: When should I use Law of Cosines instead of Law of Sines?
A: Use Law of Cosines when you know all three sides, or two sides and the included angle. Use Law of Sines when you know two angles and one side.