AAA Triangle Calculator
Calculate the third angle in a triangle and analyze triangle properties
Triangle Angle Calculator
Triangle Analysis
Example Calculations
Right Triangle Example
Given: α = 30°, β = 90°
Find: γ = ?
Solution: γ = 180° - 30° - 90° = 60°
Result: This is a 30-60-90 right triangle
Equilateral Triangle Example
Given: α = 60°, β = 60°
Find: γ = ?
Solution: γ = 180° - 60° - 60° = 60°
Result: All angles are equal (equilateral triangle)
Obtuse Triangle Example
Given: α = 100°, β = 40°
Find: γ = ?
Solution: γ = 180° - 100° - 40° = 40°
Result: One angle > 90° (obtuse triangle)
Triangle Types by Angles
Acute Triangle
All angles < 90°
Example: 70°, 60°, 50°
Right Triangle
One angle = 90°
Example: 90°, 60°, 30°
Obtuse Triangle
One angle > 90°
Example: 100°, 50°, 30°
Triangle Facts
Sum of angles always equals 180° (or π radians)
AAA triangles are similar but may have different sizes
Cannot determine side lengths from angles alone
Knowing two angles determines the third
Understanding AAA Triangles
What is an AAA Triangle?
An AAA triangle is a triangle where all three angles are known. The "AAA" stands for Angle-Angle-Angle, indicating that we have information about all three interior angles of the triangle.
The Angle Sum Property
The most fundamental property of triangles is that the sum of their interior angles always equals 180° (or π radians in the metric system). This is known as the Triangle Angle Sum Theorem.
Why Can't We Find Side Lengths?
While AAA tells us the shape of the triangle, it doesn't tell us the size. Triangles with the same angles can be scaled to any size, making them similar but not necessarily congruent.
Formula and Calculation
α + β + γ = 180°
α + β + γ = π radians
If you know two angles, you can find the third using:
γ = 180° - α - β
Applications
- •Geometry and trigonometry problems
- •Architecture and engineering design
- •Navigation and surveying
- •Computer graphics and 3D modeling