1. What is the Triangle Side Length Formula?

The triangle side length 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:

• \( a \) — Length of side a (any length units)
• \( b \) — Length of side b (same units as a)
• \( C \) — Angle between sides a and b (degrees)
• \( c \) — Length of the side opposite angle C

Explanation: The formula relates the lengths of the sides of a triangle to the cosine of one of its angles, extending the Pythagorean theorem to non-right triangles.

3. Importance of Side Length Calculation

Details: Calculating unknown side lengths is essential in various fields including engineering, architecture, navigation, and physics. It helps in solving triangles when you have partial information.

4. Using the Calculator

Tips: Enter lengths of sides a and b in any consistent units (must be positive numbers). Enter angle C in degrees (between 0 and 180). The calculator will compute the length of side c in the same units as the input sides.

5. Frequently Asked Questions (FAQ)

Q1: Can I use this for right triangles?
A: Yes, but when angle C is 90°, the formula simplifies to the Pythagorean theorem since cos(90°) = 0.

Q2: What if I know all three sides but no angles?
A: You would use the Law of Cosines in its angle form: \( \cos C = \frac{a^2 + b^2 - c^2}{2ab} \).

Q3: Does the formula work for any triangle?
A: Yes, it works for all types of triangles - acute, right, and obtuse.

Q4: What units should I use?
A: Any consistent length units can be used (meters, feet, inches, etc.), but all sides must be in the same units.

Q5: How accurate is the calculation?
A: The calculation is mathematically exact, though practical accuracy depends on the precision of your input measurements.