Solve a triangle when two sides and the included angle (SAS) are known.
Triangle Dimensions
°
Triangle Solution
10.62
Side c (Law of Cosines)
Properties calculated using the Law of Cosines and Law of Sines.
Angle A41.7°
Angle B93.3°
Area53.03
Perimeter35.62
Quick Reference
Side a10
Side b15
Angle C45°
Understanding SAS Triangles
The Side-Angle-Side (SAS) case occurs when we know the lengths of two sides and the measure of the angle between them. This information is sufficient to solve for all other properties of the triangle using the Law of Cosines and trigonometric identities.
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Pro Tips
The included angle must be the one between the two given sides.
The side opposite to angle C is calculated first using the Law of Cosines.
The sum of all angles in a triangle is always 180°.
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Fun Facts
"SAS is one of the congruence criteria; if two triangles have SAS equal, they are identical."
"The Egyptian pyramids were built using triangle principles long before the Law of Cosines was formalized."
"In navigation, SAS is used to find the distance between two points when you know the distance from a third point and the angle between them."
