1. What is an Obtuse Triangle Calculator?

Definition: This calculator computes the third side of a triangle when two sides and the included angle (greater than 90°) are known.

Purpose: It helps in solving trigonometry problems involving obtuse triangles, commonly used in engineering, architecture, and geometry.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( c \) — Length of side opposite angle C (meters)
• \( a \) — Length of first known side (meters)
• \( b \) — Length of second known side (meters)
• \( C \) — Included angle (degrees, must be >90°)

Explanation: This is a modified version of the Law of Cosines specifically for obtuse triangles (where one angle exceeds 90 degrees).

3. Importance of Obtuse Triangle Calculations

Details: Accurate calculations are essential for structural integrity in construction, land surveying, and various engineering applications where non-right-angled triangles occur.

4. Using the Calculator

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

5. Frequently Asked Questions (FAQ)

Q1: Why does the angle need to be greater than 90°?
A: This calculator specifically solves for obtuse triangles. For angles ≤90°, use the standard Law of Cosines calculator.

Q2: What units should I use?
A: The calculator uses meters for length and degrees for angles, but any consistent units will work mathematically.

Q3: Can I use this for any triangle?
A: This version is optimized for obtuse triangles. For acute triangles, the formula changes to c² = a² + b² - 2ab cos(C).

Q4: How accurate are the results?
A: Results are mathematically precise, though real-world measurements may have practical limitations.

Q5: What if I know three sides and need an angle?
A: Use the inverse formula: cos(C) = (a² + b² - c²)/(2ab), then C = arccos(result).