1. What is the Triangle Angle Calculator?

The Triangle Angle Calculator computes an angle in a triangle when given the lengths of all three sides using the cosine rule from trigonometry.

2. How Does the Calculator Work?

The calculator uses the cosine rule formula:

Where:

• \( a \) — Length of side opposite the angle (m)
• \( b \) — Length of first adjacent side (m)
• \( c \) — Length of second adjacent side (m)

Explanation: The formula calculates the angle opposite side 'a' by relating the lengths of all three sides of the triangle.

3. Importance of Angle Calculation

Details: Calculating angles from side lengths is fundamental in trigonometry and has applications in navigation, engineering, physics, and computer graphics.

4. Using the Calculator

Tips: Enter all three side lengths in meters. The values must be positive and must satisfy the triangle inequality (sum of any two sides must be greater than the third).

5. Frequently Asked Questions (FAQ)

Q1: What units should I use for the side lengths?
A: The calculator works with any consistent units (all in meters, cm, etc.), but displays results in meters. The angle result is unitless (degrees).

Q2: What if I get an error or NaN result?
A: This means the side lengths don't form a valid triangle. Check that the sum of any two sides is greater than the third.

Q3: Can I calculate other angles with this?
A: Yes, just rotate which side is 'a' to calculate different angles. The formula calculates the angle opposite the side you designate as 'a'.

Q4: How accurate is this calculation?
A: The calculation is mathematically exact, but subject to rounding errors in implementation. Results are accurate to about 6 decimal places.

Q5: Does this work for all types of triangles?
A: Yes, it works for acute, right, and obtuse triangles as long as the side lengths form a valid triangle.