Calculation of Angles in a Triangle

Angle Calculation Formulas:

\[ C = 180° - A - B \]

\[ \text{Law of Cosines} \]

Angle A:

Angle B:

Side a:

Side b:

Side c:

Angle A:

Angle B:

Angle C:

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1. What is Angle Calculation in a Triangle?

Definition: This calculator determines the unknown angles in a triangle when given either two angles or three sides.

Purpose: It helps in geometry problems, construction planning, and various engineering applications where triangle angles need to be determined.

2. How Does the Calculator Work?

The calculator uses two methods:

\[ C = 180° - A - B \]

\[ \text{Law of Cosines: } \cos A = \frac{b^2 + c^2 - a^2}{2bc} \]

Where:

\( A, B, C \) — Angles of the triangle (degrees)
\( a, b, c \) — Sides opposite to angles A, B, C respectively

Explanation:

When two angles are known, the third is calculated using the angle sum property (sum of angles = 180°).
When three sides are known, angles are calculated using the Law of Cosines.

3. Importance of Angle Calculation

Details: Knowing all angles in a triangle is essential for solving geometric problems, designing structures, and in navigation applications.

4. Using the Calculator

Tips:

Enter any two angles to find the third
OR enter all three sides to find all angles
Angles must be between 0° and 180°
Sides must be positive numbers

5. Frequently Asked Questions (FAQ)

Q1: What if I know only one angle and two sides?
A: You would need to use the Law of Sines instead. This calculator focuses on either two angles or three sides scenarios.

Q2: Why does the sum of angles equal 180°?
A: This is a fundamental property of Euclidean geometry for triangles.

Q3: Can I use this for right triangles?
A: Yes, but you could also use simpler right triangle trigonometry (Pythagorean theorem, SOHCAHTOA).

Q4: What units should I use for sides?
A: Any consistent unit (cm, m, inches, etc.) as long as all sides use the same unit.

Q5: What if my inputs don't form a valid triangle?
A: The calculator will return invalid results if the inputs violate triangle inequality or angle sum properties.