1. What is the Missing Side Length Calculator?

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

Purpose: It helps in trigonometry, geometry, and various real-world applications like construction and navigation.

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)
• \( C \) — 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 the Calculation

Details: This calculation is essential in situations where direct measurement of the third side is impractical or impossible.

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

Q3: Can I use this for any triangle?
A: Yes, it works for all types of triangles - acute, right, and obtuse.

Q4: What units should I use?
A: The calculator uses meters, but any consistent unit will work as long as all sides use the same unit.

Q5: How accurate is the result?
A: The result is mathematically exact based on your inputs. Rounding occurs only in the displayed result.