1. What is the Triangle Side Formula?

The triangle side formula (Law of Cosines) calculates the length of a side of a triangle when you know the lengths of the other two sides and the included angle. It's a fundamental formula in trigonometry and geometry.

2. How Does the Calculator Work?

The calculator uses the Law of Cosines formula:

Where:

• \( a \) — The side you're calculating (m)
• \( b \) — Known side length (m)
• \( c \) — Known side length (m)
• \( A \) — Included angle between sides b and c (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: These calculations are essential in various fields including engineering, architecture, physics, and navigation. They help solve real-world problems involving triangular measurements.

4. Using the Calculator

Tips: Enter the lengths of sides b and c in meters, and the included angle A in degrees. All values must be positive, and the angle must be between 0 and 180 degrees.

5. Frequently Asked Questions (FAQ)

Q1: Can this formula be used for any triangle?
A: Yes, the Law of Cosines works for all types of triangles - acute, right, and obtuse.

Q2: What if I know all three sides but need an angle?
A: You can rearrange the formula: \( \cos A = (b^2 + c^2 - a^2)/(2bc) \)

Q3: How accurate are the results?
A: The calculator provides results accurate to two decimal places, sufficient for most practical applications.

Q4: Does the formula work for right triangles?
A: Yes, and it simplifies to the Pythagorean theorem when the angle is 90° (since cos 90° = 0).

Q5: What units should I use?
A: The calculator uses meters for lengths, but any consistent unit can be used as long as all sides are in the same unit.