1. What is the Third Side of a 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 helps in solving triangle problems in geometry, trigonometry, and various practical applications like construction and navigation.

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)
• \( C \) — 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 calculations are essential in fields like architecture, engineering, physics, and computer graphics.

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.

5. Frequently Asked Questions (FAQ)

Q1: What is the Law of Cosines?
A: It's a formula relating the lengths of the sides of a triangle to the cosine of one of its angles, generalizing the Pythagorean theorem.

Q2: When should I use this calculator?
A: When you know two sides and the included angle (SAS) and need to find the third side of a triangle.

Q3: What if my angle is 90 degrees?
A: The formula reduces to the Pythagorean theorem (c² = a² + b²) since cos(90°) = 0.

Q4: Can I use this for any triangle?
A: Yes, it works for all types of triangles - acute, right, and obtuse.

Q5: What units should I use?
A: The calculator uses meters for length and degrees for angles, but any consistent units will work.