Triangle Angle Calculator from Sides

Angle Formula (Law of Cosines):

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

Angle C (degrees):

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is a Triangle Angle Calculator from Sides?

Definition: This calculator computes 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 to determine angles when direct measurement isn't possible.

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: Accurate angle calculation is crucial for structural integrity, proper fitting of components, and geometric analysis.

4. Using the Calculator

Tips: Enter all three side lengths in the same units (default meters). The sides must satisfy the triangle inequality theorem (sum of any two sides > third side).

5. Frequently Asked Questions (FAQ)

Q1: What if I get an error or NaN result?
A: This means the side lengths don't form a valid triangle. Check that the sum of any two sides is greater than the third.

Q2: Can I use different units?
A: Yes, as long as all three sides use the same unit (e.g., all in feet or all in meters).

Q3: Which angle does this calculate?
A: It calculates angle C, which is opposite side c. For other angles, rearrange the formula.

Q4: How accurate is this calculation?
A: The calculation is mathematically precise, but real-world accuracy depends on precise side measurements.

Q5: Can I calculate all three angles?
A: Yes, by using the formula three times, calculating each angle opposite its respective side.