AAS Triangle Calculator

Solve a triangle given two angles and a non-included side (AAS). Find all missing sides, angles, area, and perimeter.

Enter Known Values

A=40° B=60° C=80° a=5 b c
Two Known Angles (degrees)
Known Side (opposite Angle A)

Result

Enter two angles and a side, then click Calculate.

AAS Triangle: Solving with Two Angles and a Side

What is AAS?

AAS stands for "Angle-Angle-Side," where two angles and a non-included side are known. This uniquely determines the triangle.

AAS Congruence Theorem

If two angles and a non-included side of one triangle are congruent to the corresponding parts of another, the triangles are congruent. AAS is closely related to ASA since knowing two angles determines the third.

How to Solve

  1. Find angle C: C = 180° - A - B
  2. Find side b: b = a × sin(B) / sin(A)
  3. Find side c: c = a × sin(C) / sin(A)
  4. Find area: Area = ½ × b × c × sin(A)

The Law of Sines

a / sin(A) = b / sin(B) = c / sin(C)

AAS vs. ASA

  • ASA: The known side is between the two known angles (included side).
  • AAS: The known side is not between the two known angles (opposite one of them).

Both uniquely determine a triangle and are solved using essentially the same approach.

Area Formulas

  • Area = ½ × b × c × sin(A)
  • Area = ½ × a × c × sin(B)
  • Area = ½ × a × b × sin(C)
  • Heron's formula using all three sides