1. What is the Law of Cosines for Obtuse Triangles?

The Law of Cosines relates the lengths of the sides of a triangle to the cosine of one of its angles. For obtuse triangles (where one angle is greater than 90°), the formula is particularly useful as the cosine of the obtuse angle is negative.

2. How Does the Calculator Work?

The calculator uses the Law of Cosines formula:

Where:

• \( a \) — Length of side a
• \( b \) — Length of side b
• \( C \) — Obtuse angle between sides a and b (90° < C ≤ 180°)
• \( c \) — Length of side opposite angle C

Explanation: The formula accounts for the negative cosine value of obtuse angles, which results in the addition of the last term (since -2ab cos C becomes positive when cos C is negative).

3. Importance of Obtuse Triangle Calculation

Details: Calculating sides of obtuse triangles is essential in trigonometry, navigation, engineering, and physics where non-right-angled triangles frequently occur.

4. Using the Calculator

Tips: Enter lengths of sides a and b in any consistent units, and the obtuse angle C in degrees (between 90 and 180). All values must be positive.

5. Frequently Asked Questions (FAQ)

Q1: Why does the angle need to be obtuse?
A: The calculator is specifically designed for cases where the cosine is negative (90° < angle ≤ 180°), which affects the calculation differently than acute angles.

Q2: Can I use this for right triangles?
A: While the formula works for right triangles (where cos 90° = 0), it simplifies to the Pythagorean theorem. This calculator focuses on obtuse cases.

Q3: What units should I use?
A: Any consistent length units can be used (meters, feet, etc.), but all sides must be in the same units.

Q4: How accurate is the calculation?
A: The calculation is mathematically exact, though practical accuracy depends on the precision of your input values.

Q5: Can I calculate angles with this?
A: This calculator finds side lengths given two sides and the included angle. To find angles, you would need to rearrange the formula.