1. What is the Missing Triangle Side Calculator?

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

Purpose: It helps in solving oblique triangles (non-right triangles) commonly needed in trigonometry, navigation, and engineering applications.

2. How Does the Calculator Work?

The calculator uses the Law of Cosines formula:

Where:

• \( c \) — Length of the missing side (meters)
• \( a \) and \( b \) — Lengths of the known sides (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, generalizing the Pythagorean theorem.

3. Importance of the Law of Cosines

Details: The Law of Cosines is essential for solving triangles when you know:

• Two sides and the included angle (SAS)
• Three sides (SSS) when used to find angles

4. Using the Calculator

Tips: Enter the lengths of two sides and the included angle in degrees. Angle must be between 0° and 180°.

5. Frequently Asked Questions (FAQ)

Q1: When should I use Law of Cosines vs. Law of Sines?
A: Use Law of Cosines for SAS or SSS cases. Use Law of Sines for ASA or AAS cases.

Q2: What units should I use?
A: Any consistent units (meters, feet, etc.) for sides. Angle must be in degrees.

Q3: Why does angle C need to be less than 180°?
A: Angles in a triangle must sum to 180°, so no single angle can be ≥180°.

Q4: Can this calculate angles if I know all three sides?
A: Yes, but this calculator focuses on finding the missing side. Rearrange the formula to solve for angles.

Q5: What if my angle is 90°?
A: The formula reduces to the Pythagorean theorem since cos(90°) = 0.