1. What is the Length of Third Side of Triangle 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, trigonometry, construction, and various engineering applications where triangle measurements are needed.

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 side a (meters)
• \( b \) — Length of side b (meters)
• \( C \) — Angle between sides a and b (degrees)

Explanation: The formula calculates the third side by accounting for both the lengths of the known sides and the cosine of the included angle.

3. Importance of Triangle Side Calculation

Details: Accurate triangle side calculations are essential for structural integrity in construction, proper measurements in surveying, and correct solutions in trigonometry problems.

4. Using the Calculator

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

5. Frequently Asked Questions (FAQ)

Q1: What if I know all three angles but no sides?
A: You cannot determine side lengths with only angle information - you need at least one side length to use the Law of Cosines.

Q2: Can I use this for right triangles?
A: Yes, when C=90°, the formula simplifies to the Pythagorean theorem (cos(90°)=0).

Q3: What units should I use?
A: The calculator uses meters for length and degrees for angles, but any consistent units will work mathematically.

Q4: Why does angle C need to be between 0° and 180°?
A: This is the valid range for an angle in a triangle - angles outside this range wouldn't form a proper triangle.

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