1. What is the Cosine Law?

The Cosine Law (also known as the Law of Cosines) is a formula that relates the lengths of the sides of a triangle to the cosine of one of its angles. It is used to calculate an unknown side or angle in any triangle when sufficient information is known.

2. How Does the Calculator Work?

The calculator uses the Cosine Law formula:

Where:

• \( a \) — Unknown side (m)
• \( b \) — Known side (m)
• \( c \) — Known side (m)
• \( A \) — Angle opposite side a (degrees)

Explanation: The formula calculates the length of the third side of a triangle when two sides and the included angle are known.

3. Importance of Triangle Calculations

Details: Triangle calculations are fundamental in geometry, engineering, architecture, navigation, and many scientific fields. The Cosine Law is particularly useful for solving oblique triangles (non-right triangles).

4. Using the Calculator

Tips: Enter the lengths of two sides in meters, and the included angle in degrees. All values must be valid (sides > 0, angle between 0-180 degrees).

5. Frequently Asked Questions (FAQ)

Q1: When should I use the Cosine Law instead of the Pythagorean theorem?
A: Use the Cosine Law for any triangle, while the Pythagorean theorem only applies to right triangles.

Q2: Can I calculate angles using the Cosine Law?
A: Yes, the formula can be rearranged to calculate angles when all three sides are known.

Q3: What units should I use for the inputs?
A: The calculator expects side lengths in meters and angles in degrees. The result will be in meters.

Q4: Does the Cosine Law work for all types of triangles?
A: Yes, the Cosine Law applies to all triangles - acute, obtuse, and right triangles.

Q5: What if I know different combinations of sides and angles?
A: There are different formulas for different known values. This calculator specifically handles the case where two sides and the included angle are known.