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

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 (with one angle > 90°), the formula helps calculate the side opposite the obtuse angle.

2. How Does the Calculator Work?

The calculator uses the Law of Cosines:

Where:

• \( a, b \) — Adjacent sides (length units)
• \( C \) — Obtuse angle (degrees, between 90° and 180°)
• \( c \) — Side opposite angle C (length units)

Explanation: The formula accounts for the negative cosine value of obtuse angles (90° < C < 180°), which makes the last term positive.

3. Importance of Obtuse Triangle Calculation

Details: Calculating sides in obtuse triangles is essential in trigonometry, navigation, architecture, and engineering where non-right-angled triangles are common.

4. Using the Calculator

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

5. Frequently Asked Questions (FAQ)

Q1: Why does the cosine term become positive for obtuse angles?
A: For angles between 90° and 180°, cosine values are negative, making the last term positive (-2ab cos(C) becomes positive).

Q2: Can this calculator be used for acute triangles?
A: While the formula works, this calculator specifically validates that angle C is obtuse (90° < C < 180°).

Q3: What units should I use for the sides?
A: Any consistent length units (cm, m, inches, etc.) can be used as long as all sides use 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 formula?
A: This calculator specifically calculates side c given sides a, b and angle C. For angle calculations, you would rearrange the formula.