Triangle Angle Calculator (2 Sides)

Angle 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 (2 Sides)?

Definition: This calculator determines the included angle between two sides of a triangle when all three side lengths are known.

Purpose: It helps in geometry, construction, and engineering to find 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 between sides a and b (degrees)
\( a \) — Length of first side (meters)
\( b \) — Length of second side (meters)
\( c \) — Length of side opposite angle C (meters)

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 for structural integrity in construction, navigation, and various engineering applications.

4. Using the Calculator

Tips: Enter all three side lengths in meters. The calculator will determine the angle between sides a and b. All values must be > 0 and form a valid triangle.

5. Frequently Asked Questions (FAQ)

Q1: What if I get "Invalid triangle sides"?
A: This means the side lengths don't satisfy the triangle inequality theorem (sum of any two sides must be greater than the third).

Q2: Can I use different units?
A: Yes, as long as all three sides use the same unit (convert inches to meters first if needed).

Q3: How accurate is the calculation?
A: Very accurate, as it uses precise trigonometric functions. Results are shown to 2 decimal places.

Q4: What if I know two angles and need the third?
A: Simply subtract the known angles from 180° (sum of angles in a triangle is always 180°).

Q5: Can this calculate all angles of a triangle?
A: Yes, by rotating which side you enter as 'c', you can find all three angles.