SSS - Three Sides Known
Enter all three sides of the triangle to calculate angles, area, and perimeter.
About the Triangle Calculator
This triangle calculator solves triangles using the Law of Cosines and Law of Sines. Simply enter the known values (sides and angles) and get instant results for all unknown sides, angles, perimeter, and area.
Whether you're a student learning geometry, an engineer, or anyone who needs to solve triangles, this calculator provides accurate results for SSS, SAS, ASA, and AAS cases.
Triangle Solving Methods
SSS (Side-Side-Side)
When all three sides are known, use the Law of Cosines to find the angles. The calculator checks the triangle inequality theorem to ensure a valid triangle.
SAS (Side-Angle-Side)
When two sides and the included angle are known, use the Law of Cosines to find the third side, then Law of Sines for the remaining angles.
ASA (Angle-Side-Angle)
When two angles and the included side are known, find the third angle (180° - A - B), then use the Law of Sines to find the remaining sides.
AAS (Angle-Angle-Side)
When two angles and a non-included side are known, find the third angle, then use the Law of Sines to find the remaining sides.
Triangle Formulas
Law of Cosines
a² = b² + c² - 2bc × cos(A)
Law of Sines
a/sin(A) = b/sin(B) = c/sin(C)
Heron's Formula for Area
Area = sqrt(s(s-a)(s-b)(s-c))
where s = (a + b + c) / 2 (semi-perimeter)
Area Using Two Sides and Included Angle
Area = (1/2) × a × b × sin(C)
Frequently Asked Questions
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