Explore the AAA Triangle Calculator to solve for unknown sides, area, and perimeter. While knowing all three angles (AAA) defines a triangle's shape, adding one side (e.g., 'a') ensures a unique size, allowing us to find the remaining sides (b, c), total perimeter, and enclosed area using trigonometric laws.
Formula:
The AAA (Angle-Angle-Angle) criterion determines the shape of a triangle, but not its unique size. To find specific side lengths, area, and perimeter, at least one side length must also be known.
Given Angles A, B, C (such that A + B + C = 180°) and Side 'a':
- Sum of Angles:
A + B + C = 180° - Sine Rule:
a / sin(A) = b / sin(B) = c / sin(C) - Area:
Area = 0.5 * a * b * sin(C)(or similar variations) - Perimeter:
Perimeter = a + b + c
Where A, B, C are the angles in degrees, and a, b, c are the lengths of the sides opposite to angles A, B, C respectively.