AAS Triangle Calculator

Math

This AAS triangle calculator solves a triangle in the angle-angle-side case, where you know two angles and a side that is not between them. Enter Side A together with the two angles, and the calculator finds the third angle and the missing side. Because a triangle's angles always sum to 180°, the third angle is 180° minus the two you entered; the law of sines, a / sin(A) = b / sin(B), then gives the unknown side.

Formula

b = a × sin(angle2) / sin(angle1)
  • This is the AAS (angle-angle-side) case: you know two angles and a side that is not between them.
  • The third angle comes from the angle sum of a triangle: angle 3 = 180° − angle 1 − angle 2.
  • The missing side is found with the law of sines: a / sin(angle 1) = b / sin(angle 2), so b = a × sin(angle 2) / sin(angle 1).
  • Angle 1 must be the angle opposite Side A, and angle 2 the angle opposite Side B. Enter both angles in degrees.
  • The two angles you enter must add up to less than 180°, otherwise no valid triangle exists.

Example Calculation

Inputs
  • Side A: 5
  • Angle 1 (degrees): 50
  • Angle 2 (degrees): 60

With Side A = 5 and angles of 50° and 60°, the third angle is 180 − 50 − 60 = 70°. The law of sines gives Side B = 5 × sin(60°) / sin(50°) ≈ 5.65.

Frequently asked questions

What does AAS mean in a triangle?
AAS stands for angle-angle-side. You know two of the triangle's angles and one side that is not between them, and you want to find the remaining side and angle.
How does this calculator solve an AAS triangle?
It first finds the third angle as 180° minus the two known angles, then applies the law of sines, b = a × sin(angle 2) / sin(angle 1), to find the unknown side.
Which angle goes with which side?
Angle 1 is the angle opposite the side you enter (Side A), and angle 2 is the angle opposite the side being found (Side B). Keeping this pairing correct is essential for the law of sines.
What units should I use for the angles?
Enter the angles in degrees. The calculator converts them to radians internally before applying the sine function.
Why am I getting an unrealistic result?
Check that your two angles add up to less than 180°. If they sum to 180° or more the triangle cannot exist, and the law of sines will not give a meaningful side length.