1. What is the Triangle Side Calculation?

The triangle side calculation uses the Law of Cosines to determine the length of the third side of a triangle when two sides and the included angle are known. This is essential for solving oblique triangles in trigonometry.

2. How Does the Calculator Work?

The calculator uses the Law of Cosines formula:

Where:

• \( a \) — Length of side a
• \( b \) — Length of side b
• \( C \) — Included angle between sides a and b (in degrees)
• \( c \) — Length of the calculated side

Explanation: The formula relates the lengths of the sides of a triangle to the cosine of one of its angles, extending the Pythagorean theorem to non-right triangles.

3. Importance of Triangle Calculations

Details: Accurate triangle calculations are crucial for geometry, trigonometry, navigation, engineering, and physics applications where triangular relationships need to be determined.

4. Using the Calculator

Tips: Enter the lengths of two sides and the included angle in degrees. All values must be positive numbers, and the angle must be between 0 and 180 degrees.

5. Frequently Asked Questions (FAQ)

Q1: Can this calculator be used for right triangles?
A: Yes, when angle C is 90°, the formula simplifies to the Pythagorean theorem (cos 90° = 0).

Q2: What units should I use for the side lengths?
A: Any consistent unit can be used (cm, m, inches, etc.) as long as both sides are in the same unit.

Q3: What if I know three sides and need an angle?
A: The Law of Cosines can be rearranged to solve for angles: \( \cos C = \frac{a² + b² - c²}{2ab} \).

Q4: Are there limitations to this formula?
A: The formula works for all triangles, but ensure the angle is between the two given sides for meaningful results.

Q5: How accurate are the results?
A: Results are mathematically precise based on the inputs, though real-world measurements may have practical limitations.