Calculate Angle of Triangle Given 3 Sides

Angle Formula (Law of Cosines):

\[ C = \arccos\left(\frac{a^2 + b^2 - c^2}{2ab}\right) \]

Angle C (degrees):

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1. What is the Angle of Triangle Calculator?

Definition: This calculator determines an angle of a triangle when all three side lengths are known, using the Law of Cosines.

Purpose: It helps in geometry, engineering, and construction when you need to find angles from side measurements.

2. How Does the Calculator Work?

The calculator uses the Law of Cosines formula:

\[ C = \arccos\left(\frac{a^2 + b^2 - c^2}{2ab}\right) \]

Where:

\( C \) — Angle opposite side c (degrees)
\( a, b, c \) — Lengths of the triangle sides (meters)

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

3. Importance of Angle Calculation

Details: Knowing all angles is essential for proper triangle construction, structural analysis, and various engineering applications.

4. Using the Calculator

Tips: Enter all three side lengths in meters. The angle opposite side c will be calculated. All values must be > 0 and must satisfy the triangle inequality.

5. Frequently Asked Questions (FAQ)

Q1: What is the triangle inequality?
A: The sum of any two sides must be greater than the third side (a + b > c, a + c > b, b + c > a).

Q2: Why does my input return no result?
A: Either the values don't form a valid triangle, or the calculation would result in an invalid cosine value.

Q3: Can I calculate other angles with this?
A: Yes, just rotate which side is 'c' in the formula to find different angles.

Q4: What's the range of possible angles?
A: In a valid triangle, angles range from >0° to <180°.

Q5: How accurate is the calculation?
A: The calculation is mathematically precise, though displayed with 2 decimal places for readability.