1. What is the Missing Length of Triangle Formula?

Definition: This calculator finds the missing side of a triangle when you know two sides and the included angle using the Law of Cosines.

Purpose: It helps in solving oblique triangles (non-right triangles) in geometry, trigonometry, and various real-world 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 known side a (meters)
• \( b \) — Length of known 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 construction, navigation, physics, and engineering where triangular relationships are common.

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: 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: The calculator uses meters for length and degrees for angles, but any consistent units will work.

Q5: Why does angle C need to be between 0° and 180°?
A: This is the valid range for angles in a Euclidean triangle - angles can't be negative or make a straight line.