1. What is the Missing Side of a Triangle Calculator?

Definition: This calculator finds the length of the third side of a triangle when two sides and the included angle are known.

Purpose: It helps in solving triangles for geometry problems, construction planning, and various engineering applications.

2. How Does the Calculator Work?

The calculator uses the Law of Cosines formula:

Where:

• \( c \) — Length of the missing side (meters)
• \( a \) — Length of the first known side (meters)
• \( b \) — Length of the 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 calculations are essential for structural integrity in construction, navigation, 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: When should I use the Law of Cosines?
A: Use it when you know two sides and the included angle (SAS) or all three sides (SSS) of a triangle.

Q2: What's the difference between Law of Cosines and Law of Sines?
A: Law of Sines relates sides to opposite angles, while Law of Cosines relates all three sides to one angle.

Q3: Can I use this for right triangles?
A: Yes, but when angle C is 90°, the formula simplifies to the Pythagorean theorem (cos(90°) = 0).

Q4: What units should I use?
A: Any consistent units (meters, feet, etc.) can be used as long as all side lengths are in the same unit.

Q5: Why does angle C need to be less than 180°?
A: In Euclidean geometry, a triangle's angles must sum to 180°, so no single angle can be 180° or more.