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

The Law of Cosines is a formula that relates the lengths of the sides of a triangle to the cosine of one of its angles. It's particularly useful for solving obtuse triangles where one angle is greater than 90 degrees.

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
• \( C \) — Angle between sides a and b (in degrees)
• \( c \) — Length of the missing side opposite angle C

Explanation: The formula calculates the length of the third side when you know two sides and the included angle.

3. Importance of Calculating Missing Sides

Details: Calculating missing sides in obtuse triangles is essential for various applications in trigonometry, engineering, physics, and navigation.

4. Using the Calculator

Tips: Enter the lengths of two sides and the included angle in degrees. All values must be positive numbers (sides > 0, angle between 0-180 degrees).

5. Frequently Asked Questions (FAQ)

Q1: Can this calculator be used for acute triangles?
A: Yes, the Law of Cosines works for all triangles, but it's particularly useful for obtuse triangles where the Pythagorean theorem doesn't apply.

Q2: What units should I use for the sides?
A: Any consistent length units can be used (cm, m, inches, etc.), just ensure all sides use the same units.

Q3: How accurate is the calculation?
A: The calculation is mathematically precise, though results are rounded to two decimal places for readability.

Q4: What if I know three sides and need an angle?
A: The Law of Cosines can be rearranged to solve for angles, but this calculator is specifically for finding missing sides.

Q5: Does the angle have to be in degrees?
A: This calculator expects degrees, but the formula works with radians if properly converted.