What are the four triangle solving cases?

SSS (three sides), SAS (side-angle-side), AAS (angle-angle-side), and ASA (angle-side-angle).

Can AAA (three angles) determine a unique triangle?

No, AAA only gives shape but not size. Infinitely many similar triangles share the same angles.

What is the ambiguous case in triangle solving?

SSA (side-side-angle) can have 0, 1, or 2 solutions depending on the values—it's ambiguous and requires careful analysis.

Mathematics

Triangle Solver

Enter known values (SSS, AAS, ASA). Angles in degrees.

Side a

Side b

Side c

Angle A (°)

Angle B (°)

Angle C (°)

A triangle solver computes all unknown sides and angles of a triangle from the known values. It handles SSS (three sides), AAS/ASA (two angles and one side), and SAS cases.

Symbol	Name	Unit	Description
a, b, c	side lengths	length	—
A, B, C	angles opposite to sides a, b, c	degrees	—

Known	Method	First Step
SSS	Law of Cosines	Find largest angle first
AAS	Law of Sines	Find third angle (180−sum)
ASA	Law of Sines	Find third angle first
SAS	Law of Cosines	Find opposite side

References

›Triangle solver — Khan Academy

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Solve any triangle given 3 known values. Formula, variable legend, diagram and worked example included. Instant geometry result.

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