1. What is an AAA Triangle?

An AAA (Angle-Angle-Angle) triangle is defined by its three angles. While AAA determines the shape of a triangle, it doesn't determine its size - AAA triangles are always similar (same shape but possibly different sizes).

2. How Does the Calculator Work?

The calculator uses the Law of Sines to determine side lengths when one side length is known:

Where:

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

Explanation: The Law of Sines relates the ratios of side lengths to the sines of their opposite angles. Given three angles and one side, we can calculate the other sides.

3. Importance of AAA Triangle Calculation

Details: Calculating side lengths from angles is crucial in trigonometry, navigation, architecture, and engineering when only angular measurements are available.

4. Using the Calculator

Tips: Enter all three angles (must sum to 180°), the length of one known side, and specify which side it is. The calculator will determine the other two side lengths.

5. Frequently Asked Questions (FAQ)

Q1: Why can't AAA alone determine exact side lengths?
A: AAA only determines the shape (angles) but not the size. You need at least one side length to determine the actual size of the triangle.

Q2: What if my angles don't sum to exactly 180°?
A: The calculator will show an error. The sum must be exactly 180° for a valid Euclidean triangle.

Q3: Can I use this for right triangles?
A: Yes, right triangles are a special case where one angle is 90°.

Q4: What units should I use?
A: Angles should be in degrees, side length can be any unit as long as you're consistent.

Q5: How precise are the results?
A: Results are precise to 4 decimal places, but remember that measurement errors in angles will affect accuracy.