AAS Triangle Calculator
Solve Angle-Angle-Side triangles. Enter two angles and a non-included side to find all other measurements.
Enter AAS Values
AAS Triangle:
Two angles and a non-included side (a side that is not between the two angles) are known.
Solution Method:
1. Find angle C: C = 180° - A - B
2. Use Law of Sines to find sides b and c
3. Calculate area and perimeter
Frequently Asked Questions
What is an AAS triangle?
AAS stands for Angle-Angle-Side. It's a triangle where you know two angles and a side that is NOT between them (a non-included side). This is equivalent to ASA because once you know two angles, the third angle is determined, making AAS and ASA essentially the same case.
How do you solve an AAS triangle?
First, find the third angle using the fact that all angles sum to 180°. Then, use the Law of Sines (sin(A)/a = sin(B)/b = sin(C)/c) to find the two unknown sides. Since you know one side and all three angles, you can calculate everything.
What's the difference between AAS and ASA?
In AAS, the known side is NOT between the two known angles, while in ASA, the known side IS between the two known angles. However, both lead to unique triangles and are solved using the same mathematical approach - angle sum and Law of Sines.
Is AAS a valid triangle congruence condition?
Yes! AAS is one of the fundamental triangle congruence conditions. If two triangles have two pairs of equal angles and a pair of equal corresponding non-included sides, the triangles are congruent. This is because knowing two angles determines the third angle.
Can an AAS triangle have no solution?
An AAS triangle will have no solution if the two given angles sum to 180° or more (leaving no room for a valid third angle), or if any given value is zero, negative, or otherwise invalid (like an angle greater than 180°).
Why does knowing two angles determine the third?
In Euclidean geometry, the sum of all three angles in a triangle must equal exactly 180°. Therefore, if you know two angles, you can calculate the third: C = 180° - A - B. This is a fundamental property of triangles in flat (Euclidean) space.
What if I enter angles that sum to exactly 180°?
If the two angles you enter sum to exactly 180°, there's no room for a third angle (it would be 0°), so the triangle degenerates into a straight line. The calculator will indicate this as an error since it's not a valid triangle.
Can I solve right triangles with AAS?
Yes! If one of your angles is 90°, you can still use AAS to solve the triangle. However, for right triangles, basic trigonometric ratios (sin, cos, tan) might be simpler. The AAS method using Law of Sines will still give you correct results.