Compute missing triangle measures from standard input combinations. Review steps, exports, graphs, and examples easily. Ideal for homework practice and calculator verification sessions daily.
Use side labels opposite matching angles, just like standard triangle notation.
| Mode | Inputs | Area | Perimeter | Triangle Type |
|---|---|---|---|---|
| SSS | a = 3, b = 4, c = 5 | 6 | 12 | Right Scalene |
| SAS | a = 7, b = 8, C = 60° | 24.2487 | 22.5498 | Acute Scalene |
| Right Triangle | a = 5, b = 12 | 30 | 30 | Right Scalene |
This page helps you solve triangles from several common input patterns. It works well for homework review, quick geometry checks, and calculator verification. The notation follows the standard convention: side a is opposite angle A, side b is opposite angle B, and side c is opposite angle C.
The calculator supports SSS, SAS, ASA or AAS, SSA, and right-triangle solving. That makes it useful for many classroom cases, including the ambiguous SSA case that can produce two valid answers. When two solutions exist, both solutions appear in separate result blocks.
Along with the missing sides and angles, the tool also returns area, perimeter, semiperimeter, inradius, circumradius, altitudes, and medians. These extra outputs help when you want more than a basic answer and need a fuller geometric summary.
The graph section plots the solved triangle using coordinate geometry. This gives a quick visual check and can help you compare whether the solved shape matches your expectations. The CSV and PDF buttons make it easier to save results for notes, assignments, or revision sheets.
Law of Cosines: This is used in SSS and SAS cases.
c² = a² + b² − 2ab cos(C)
a² = b² + c² − 2bc cos(A)
b² = a² + c² − 2ac cos(B)
Law of Sines: This is used in ASA, AAS, and SSA cases.
a / sin(A) = b / sin(B) = c / sin(C)
Heron’s Formula: This is used to find area from three sides.
s = (a + b + c) / 2
Area = √(s(s − a)(s − b)(s − c))
Right Triangle Rule: This is used in the right-triangle mode.
c² = a² + b²
Other Measures:
Perimeter = a + b + c
Inradius = Area / s
Circumradius = abc / (4 × Area)
Altitude to side a = 2 × Area / a
It supports SSS, SAS, ASA or AAS, SSA, and right-triangle cases. That covers most classroom triangle-solving situations and many calculator checking tasks.
Yes. The SSA case can be ambiguous. If two valid triangles exist, the calculator displays both solutions separately so you can compare them clearly.
Yes. Select radians in the angle unit field before entering angles. The final solved angles are still shown in degrees for easy reading.
The graph shows the solved triangle in coordinate form. It helps confirm side relationships, overall shape, and whether the result matches your expected geometry.
The graph uses a standard coordinate setup for easy plotting. Side c is placed on the horizontal axis, and the third vertex is calculated from the solved dimensions.
Besides sides and angles, the calculator returns area, perimeter, semiperimeter, inradius, circumradius, altitudes, medians, and triangle classifications.
Yes. After solving a triangle, you can export the result table as a CSV file or create a PDF summary directly from the page.
Avoid impossible side lengths, angle sums of 180 degrees or more, and a hypotenuse smaller than a leg. Invalid combinations will show an error message.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.