1. What is the Obtuse Angle Formula?

The formula calculates an angle in a triangle when all three sides are known, using the Law of Cosines. It's particularly useful for finding obtuse angles (greater than 90 degrees) in triangles.

2. How Does the Calculator Work?

The calculator uses the Law of Cosines formula:

Where:

• \( a, b \) — Adjacent sides to the angle
• \( c \) — Side opposite the angle
• \( C \) — The angle being calculated

Explanation: The formula relates the lengths of the sides of a triangle to the cosine of one of its angles.

3. Importance of Angle Calculation

Details: Calculating angles in triangles is fundamental in geometry, engineering, architecture, and various fields of science. The Law of Cosines is particularly important for solving triangles that aren't right-angled.

4. Using the Calculator

Tips: Enter all three side lengths in the same units. The side opposite the angle you're calculating should be entered as 'Side c'. Choose whether you want the result in degrees or radians.

5. Frequently Asked Questions (FAQ)

Q1: What makes an angle obtuse?
A: An obtuse angle is greater than 90 degrees but less than 180 degrees.

Q2: Can this calculator work for acute angles?
A: Yes, the formula works for all angles in any triangle, not just obtuse ones.

Q3: What if my triangle doesn't exist with these side lengths?
A: The calculator will still give a result, but it might not correspond to a valid triangle. Ensure the sum of any two sides is greater than the third.

Q4: Why would I want the result in radians?
A: Radians are often used in higher mathematics, physics, and computer graphics calculations.

Q5: Can this be used for right triangles?
A: Yes, though for right triangles the Pythagorean theorem is often simpler.