1. What is the Law of Cosines?

The Law of Cosines is a formula relating the lengths of the sides of a triangle to the cosine of one of its angles. For obtuse triangles (where one angle > 90°), it's particularly useful for finding the side opposite the obtuse angle.

2. How Does the Calculator Work?

The calculator uses the Law of Cosines formula:

Where:

• \( a, b \) — Known sides of the triangle
• \( C \) — Obtuse angle between sides a and b (>90°)
• \( c \) — Side opposite angle C (calculated)

Explanation: The formula accounts for the decreased cosine value in obtuse angles, which results in the third side being longer than in acute triangles.

3. Importance of Obtuse Triangle Calculations

Details: Calculating sides in obtuse triangles is essential in various fields including engineering, architecture, and navigation where non-right-angled triangles frequently occur.

4. Using the Calculator

Tips: Enter the lengths of two sides and the included obtuse angle (between 90° and 180°). All values must be positive numbers with angle C strictly greater than 90°.

5. Frequently Asked Questions (FAQ)

Q1: Why does the angle need to be greater than 90°?
A: This calculator is specifically designed for obtuse triangles. For acute triangles, the same formula applies but the cosine value will be positive.

Q2: What units should I use?
A: Any consistent length units can be used (cm, m, inches, etc.) as long as both sides are in the same units.

Q3: Can I use this for right triangles?
A: While technically correct when C=90° (cos(90°)=0 reduces to Pythagorean theorem), this calculator is optimized for obtuse triangles.

Q4: What if I know three sides and want to find an angle?
A: The Law of Cosines can be rearranged to solve for angles, but this calculator only solves for the third side.

Q5: How accurate are the results?
A: Results are mathematically exact based on the inputs, though practical accuracy depends on measurement precision of your inputs.