Triangle Angle Calculator 3 Sides

Angle Calculation Formula:

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

Angle C (degrees):

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1. What is a Triangle Angle Calculator (3 Sides)?

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, trigonometry, and various engineering applications where triangle measurements are needed.

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

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

3. Importance of Triangle Angle Calculation

Details: Accurate angle calculation is essential in construction, navigation, computer graphics, and any field requiring precise geometric measurements.

4. Using the Calculator

Tips: Enter all three side lengths in the same units. The calculator will verify if the sides can form a valid triangle before computing the angle.

5. Frequently Asked Questions (FAQ)

Q1: What units should I use for the sides?
A: Any consistent unit (meters, feet, etc.) can be used as long as all three sides use the same unit.

Q2: Why does my input return an error?
A: The sides must satisfy the triangle inequality: sum of any two sides must be greater than the third side.

Q3: Can I calculate other angles with this?
A: Yes, rearrange the formula by changing which side is opposite the angle you want to find.

Q4: How accurate is the calculation?
A: The calculator provides results accurate to two decimal places, sufficient for most practical applications.

Q5: What if I need angles in radians?
A: Multiply the degree result by π/180 to convert to radians.