1. What is the Pythagorean Theorem with Angles?

The Pythagorean theorem relates the sides of a right triangle. This extension uses the law of cosines to calculate angles in any triangle when all three sides are known.

2. How Does the Calculator Work?

The calculator uses the law of cosines formula:

Where:

• \( a \) — Length of side adjacent to angle θ
• \( b \) — Length of side opposite angle θ
• \( c \) — Length of the third side
• \( \theta \) — Angle between sides a and c (in degrees)

Explanation: The formula calculates the angle opposite to side b using the relationship between all three sides of the triangle.

3. Importance of Angle Calculation

Details: Calculating angles in triangles is fundamental in geometry, engineering, physics, and many practical applications like construction and navigation.

4. Using the Calculator

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

5. Frequently Asked Questions (FAQ)

Q1: Does this work for right triangles?
A: Yes, it works for all triangles - right, acute, and obtuse. For right triangles, it simplifies to basic trigonometric functions.

Q2: What units should I use?
A: Any consistent units (cm, m, inches, etc.) as long as all three sides use the same unit.

Q3: Why might I get an error?
A: Errors occur when the side lengths don't form a valid triangle (violating triangle inequality theorem) or when values are non-positive.

Q4: Can I calculate other angles with this?
A: Yes, just rearrange which side is considered 'b' in the formula to calculate different angles.

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