AAS Triangle Calculator

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Solve a triangle when two angles and one non-included side are known.

Known Parameters

Angle A (°)

Angle B (°)

Side a (opposite to A)

Solved Triangle

105.00°

Angle C

Side b (opposite to B)14.14

Side c (opposite to C)19.32

Area68.30

Perimeter43.46

About this calculator

The AAS Scenario

The AAS (Angle-Angle-Side) case involves knowing two angles and a side that is opposite to one of those angles. Because the sum of angles is always 180°, we can immediately find the third angle. Then, we use the Law of Sines to find the remaining sides.

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Pro Tips

Find Angle C first: C = 180° - A - B.
Use the known side and its opposite angle as the base ratio for the Law of Sines.
Side length must be positive, and the sum of given angles must be less than 180°.

Fun Facts

"The Law of Sines works for any triangle, not just right-angled ones."
"AAS is one of the conditions for triangle congruence."
"Arab mathematicians in the 10th century greatly expanded the usage of sine rules for spherical trigonometry to aid in navigation."

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