1. What is a Triangle Third Side Calculator?

Definition: This calculator determines the length of the third side of a triangle when you know two sides and the included angle.

Purpose: It's useful for geometry problems, construction planning, and any application requiring triangle side calculations.

2. How Does the Calculator Work?

The calculator uses the Law of Cosines formula:

Where:

• \( c \) — Length of the third side (meters)
• \( a \) — Length of first known side (meters)
• \( b \) — Length of second known side (meters)
• \( C \) — Included angle between sides a and b (degrees)

Explanation: The formula relates the lengths of the sides of a triangle to the cosine of one of its angles.

3. Importance of Triangle Calculations

Details: Accurate triangle side calculations are essential in construction, navigation, engineering, and various scientific applications.

4. Using the Calculator

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

5. Frequently Asked Questions (FAQ)

Q1: What if I know three angles but no sides?
A: You cannot determine side lengths with only angle information - triangles with the same angles can be different sizes.

Q2: Does this work for any type of triangle?
A: Yes, the Law of Cosines works for all triangles - acute, right, and obtuse.

Q3: What's the special case for right triangles?
A: When angle C is 90°, the formula simplifies to the Pythagorean theorem: \( c = \sqrt{a² + b²} \).

Q4: How accurate are the results?
A: Results are mathematically precise, though practical accuracy depends on your input measurements.

Q5: Can I calculate angles with this?
A: No, this calculates side lengths. Use the Law of Cosines rearranged to calculate angles if needed.