Calculate Angle from Two Sides of Triangle

Angle Calculation Formula:

\[ C = \arccos\left(\frac{a² + b² - c²}{2ab}\right) \]

Angle C:

degrees

Definition: This calculator determines the angle opposite to side c in a triangle when all three side lengths are known.

Purpose: It helps in trigonometry, geometry, and various engineering applications where triangle measurements are needed.

The calculator uses the Law of Cosines formula:

\[ C = \arccos\left(\frac{a² + b² - c²}{2ab}\right) \]

Where:

Explanation: The formula calculates the angle by relating the lengths of all three sides of the triangle.

Details: Accurate angle calculation is essential in construction, navigation, computer graphics, and various scientific applications.

Tips: Enter all three side lengths in meters. The triangle inequality must hold (sum of any two sides > third side).

Q1: What if I get "NaN" as result?
A: This means the input side lengths don't form a valid triangle (violate triangle inequality theorem).

Q2: Can I use this for any triangle?
A: Yes, this works for all triangle types (acute, right, obtuse).

Q3: What units should I use?
A: The calculator uses meters, but any consistent unit will work as long as all sides use the same unit.

Q4: How accurate is the calculation?
A: The calculation is mathematically precise, limited only by floating-point precision.

Q5: Can I calculate other angles with this?
A: Yes, just rearrange the sides to make the desired angle opposite to side c.