SSS
Side — Side — Side
You know all three side lengths of the triangle.
Example: a = 5, b = 4, c = 3
Nut uses: Law of Cosines
NUT ENGINEERING TOOLS
General Triangle Solver
See It. Solve It. Understand It.
Enter any valid combination of sides and angles. Nut identifies the triangle case and solves the remaining geometry.
Live Geometry
Diagram will adjust to the solved triangle.
Enter What You Know
Enter any valid combination of three known values, including at least one side.
SSA
Ambiguous Case Solutions
These measurements create two valid triangles. Select either solution to compare the geometry.
02
Calculated Results
Complete triangle geometry and identified solve case.
Side a
—
Angle A
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Side b
—
Angle B
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Side c
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Angle C
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Area
—
Solve Case
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03
Your Solution
Nut shows which triangle method was used and walks through the calculation step by step.
Enter a valid triangle combination and press Solve Triangle to see the calculation steps.
04
Understanding Triangle Combinations
The letters S and A describe what information you already know: S = Side and A = Angle.
SAS
Side — Angle — Side
You know two sides and the angle located between those two sides. This is called the included angle.
Example: b = 4, A = 90°, c = 3
Nut uses: Law of Cosines
ASA
Angle — Side — Angle
You know two angles and the side located between those angles. The third angle is found because all three angles total 180°.
Example: A = 90°, c = 3, B = 53.13°
Nut uses: Angle Sum + Law of Sines
AAS
Angle — Angle — Side
You know two angles and a side that is not between those two angles. The missing angle is found first.
Example: A = 90°, C = 36.87°, b = 4
Nut uses: Angle Sum + Law of Sines
SSA
Side — Side — Angle
You know two sides and an angle that is not between the two known sides.
SSA is special because the same measurements can sometimes create two different valid triangles. This is called the ambiguous case.
Example: A = 30°, a = 5, b = 8
Nut uses: Law of Sines + ambiguity check
SSA can produce 0, 1, or 2 valid triangles. Nut checks all
possibilities rather than assuming only one solution.
05
How It Works
General triangles are solved using combinations of angle relationships, the Law of Sines, and the Law of Cosines.
A + B + C = 180°
Angle Sum
The three interior angles of every triangle total 180 degrees.
a / sin(A) = b / sin(B) = c / sin(C)
Law of Sines
Used when an angle-side opposite pair is known.
c² = a² + b² − 2ab cos(C)
Law of Cosines
Used for SSS and SAS triangle cases.
Nut Industries V2 — Development Preview