1. What is the Law of Cosines?

The Law of Cosines relates the lengths of the sides of a triangle to the cosine of one of its angles. It's particularly useful for solving triangles when you know two sides and the included angle (SAS).

2. How Does the Calculator Work?

The calculator uses the Law of Cosines:

Where:

• \( a \) — Length of side a (converted to inches)
• \( b \) — Length of side b (converted to inches)
• \( C \) — Included angle between sides a and b (in degrees)
• \( c \) — Calculated length of side c (converted back to feet and inches)

Explanation: The formula calculates the third side of a triangle when two sides and the included angle are known.

3. Importance of Triangle Calculations

Details: Accurate triangle calculations are essential in fields like construction, engineering, and surveying where precise measurements are critical.

4. Using the Calculator

Tips: Enter side lengths in feet and inches, and the included angle in degrees. All values must be valid (positive lengths, angle between 0-180 degrees).

5. Frequently Asked Questions (FAQ)

Q1: Can I use this for right triangles?
A: Yes, but the Pythagorean theorem would be simpler for right triangles (when angle C = 90°).

Q2: What units does this calculator use?
A: The calculator works with feet and inches for input and output.

Q3: How precise are the results?
A: Results are precise to two decimal places for the inches portion.

Q4: Can I calculate angles with this?
A: No, this calculator only finds the third side when two sides and the included angle are known.

Q5: What if my angle is exactly 0° or 180°?
A: The triangle would degenerate into a straight line in these cases.