Exterior Angles of a Triangle Calculator With Sides

Exterior Angle Calculation:

\[ \text{Exterior Angle} = 180° - \text{Interior Angle} \] \[ \text{Interior Angle from Law of Cosines:} \] \[ \cos(A) = \frac{b^2 + c^2 - a^2}{2bc} \]

Exterior Angle at A:

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1. What is an Exterior Angle?

An exterior angle of a triangle is formed by one side of the triangle and the extension of an adjacent side. The measure of an exterior angle equals the sum of the measures of the two non-adjacent interior angles.

2. How Does the Calculator Work?

The calculator uses the following formulas:

\[ \text{Exterior Angle} = 180° - \text{Interior Angle} \] \[ \cos(A) = \frac{b^2 + c^2 - a^2}{2bc} \]

Where:

\( a, b, c \) — Sides of the triangle
\( A \) — Interior angle opposite side a
The exterior angle is calculated at vertex A

Explanation: First calculates the interior angle using the Law of Cosines, then subtracts from 180° to get the exterior angle.

3. Importance of Exterior Angles

Details: Exterior angles are important in geometry for understanding triangle properties, proving theorems, and solving practical problems in engineering and architecture.

4. Using the Calculator

Tips: Enter all three side lengths in the same units. Values must be positive and satisfy the triangle inequality theorem (sum of any two sides must be greater than the third).

5. Frequently Asked Questions (FAQ)

Q1: What's the sum of exterior angles of a triangle?
A: The sum of all three exterior angles (one at each vertex) is always 360°.

Q2: Can I calculate exterior angles with just side lengths?
A: Yes, this calculator shows how to do it using the Law of Cosines to first find interior angles.

Q3: What if my sides don't form a valid triangle?
A: The calculator will not provide valid results if the input values violate the triangle inequality theorem.

Q4: How precise are the results?
A: Results are accurate to one decimal place, but precision depends on accurate input measurements.

Q5: Can this calculate all three exterior angles?
A: This calculates the exterior angle at vertex A. Repeat the process for other vertices by rotating the side inputs.