1. What is the Obtuse Triangle Formula?

Definition: This formula calculates the third side (c) of an obtuse triangle when you know two sides (a, b) and the included obtuse angle (C > 90°).

Purpose: It helps in solving triangles in trigonometry, engineering, and construction where one angle is greater than 90 degrees.

2. How Does the Formula Work?

The formula is derived from the Law of Cosines:

Where:

• \( c \) — Length of side opposite angle C (meters)
• \( a, b \) — Lengths of the other two sides (meters)
• \( C \) — Obtuse angle between sides a and b (degrees, must be > 90°)

Explanation: The formula relates the lengths of the sides of a triangle to the cosine of one of its angles.

3. Importance of the Obtuse Triangle Formula

Details: This formula is essential for solving real-world problems involving non-right triangles, particularly in surveying, navigation, and structural engineering.

4. Using the Calculator

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

5. Frequently Asked Questions (FAQ)

Q1: Why does angle C need to be greater than 90°?
A: This calculator specifically solves for obtuse triangles (one angle > 90°). For acute triangles, the formula works but the cosine term becomes positive.

Q2: Can I use this for right triangles?
A: When C = 90°, this becomes the Pythagorean theorem (cos(90°) = 0).

Q3: What units should I use?
A: Use consistent units (meters shown here, but any length unit works as long as all sides use the same unit).

Q4: How accurate is this calculation?
A: Very accurate, provided your input values are precise. The calculation uses double-precision floating point arithmetic.

Q5: What if I know three sides and need to find an angle?
A: Rearrange the formula to solve for angle C: \( C = \arccos\left(\frac{a^2 + b^2 - c^2}{2ab}\right) \)