You entered 3 sides of a triangle.
Find the 3 angles using SSS method.
We need to check the largest angle first.
See if we have an obtuse angle
This is Side 1 Using Law of Cosines:
Find Angle 1 Using Law of Cosines
Take Arccosine of the following:| Angle 1 = | Side 22 + Side 32 - Side 12 |
| 2 * Side 2 * Side 3 |
| Angle 1 = | 8.48532 + 6.32462 - 122 |
| 2 * 8.4853 * 6.3246 |
| Angle 1 = | 72.00031609 + 40.00056516 - 144 |
| 107.33225676 |
| Angle 1 = | -31.99911875 |
| 107.33225676 |
Angle 1 = Arccos(-0.29813142587276)
Angle 1 = 107.345°
Find Angle 3 Using Law of Cosines
Take Arccosine of the following:| Angle 3 = | Side 12 + Side 22 - Side 32 |
| 2 * Side 1 * Side 2 |
| Angle 3 = | 122 + 8.48532 - 6.32462 |
| 2 * 12 * 8.4853 |
| Angle 3 = | 144 + 72.00031609 - 40.00056516 |
| 203.6472 |
| Angle 3 = | 175.99975093 |
| 203.6472 |
Angle 3 = Arccos(0.86423850133957)
Angle 3 = 30.204°
Now solve for Angle 2
The sum of angles n a triangle = 180
Missing Angle = 180 - sum of 2 angles
Angle 2 = 180 - (Angle1 + Angle 3)
Angle 2 = 180 - (107.34540674467 + 30.20413451409)
Angle 2 = 180 - 137.54954125876
Angle 2 = 42.45°
Calculate Semi-Permieter (s)
Use Heron's formula| s = | Side1 + Side2 + Side3 |
| 2 |
| s = | 12 + 8.4853 + 6.3246 |
| 2 |
| s = | 26.8099 |
| 2 |
s = 13.405
Calculate Area (A)
Use Heron's formulaA = √s * (s - side1) * (s - side2) * (s - side3)
A = √13.405 * (13.405 - 12) * (13.405 - 8.4853) * (13.405 - 6.3246)
A = √13.405 * (1.405) * (4.9197) * (7.0804)
A = √656.05395287202
A = 25.614
Classify this triangle:
Since no sides equal each otherthis is a Scalene Triangle
Since no sides equal each other
this is a Scalene Triangle
this is a Scalene Triangle
You have 2 free calculationss remaining
What is the Answer?
Since no sides equal each other
this is a Scalene Triangle
this is a Scalene Triangle
How does the Triangle Solver and Classify Triangles Calculator work?
Free Triangle Solver and Classify Triangles Calculator - Solves a triangle including area using the following solving methods
Side-Angle-Side (SAS) Side Angle Side
Angle-Side-Angle (ASA) Angle Side Angle
Side-Side-Angle (SSA) Side Angle Side
Side-Side-Side (SSS) Side Side Side
Area (A) is solved using Herons Formula
Law of Sines
Law of Cosines
Also classifies triangles based on sides and angles entered.
This calculator has 1 input.
Side-Angle-Side (SAS) Side Angle Side
Angle-Side-Angle (ASA) Angle Side Angle
Side-Side-Angle (SSA) Side Angle Side
Side-Side-Side (SSS) Side Side Side
Area (A) is solved using Herons Formula
Law of Sines
Law of Cosines
Also classifies triangles based on sides and angles entered.
This calculator has 1 input.
What 6 formulas are used for the Triangle Solver and Classify Triangles Calculator?
Acute Triangle = All angles < 90°
Right Triangle = One Angle = 90°
Obtuse Triangle = One angle > 90°
Equilateral Triangle = All sides equal
Isosceles Triangle = 2 sides equal
Scalene Triangle = No sides equal
For more math formulas, check out our Formula Dossier
Right Triangle = One Angle = 90°
Obtuse Triangle = One angle > 90°
Equilateral Triangle = All sides equal
Isosceles Triangle = 2 sides equal
Scalene Triangle = No sides equal
For more math formulas, check out our Formula Dossier
What 6 concepts are covered in the Triangle Solver and Classify Triangles Calculator?
- angle
- the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle.
- area
- Number of square units covering the shape
- heron
- side
- line segment joining two vertices in a polygon also known as an edge
- triangle
- a flat geometric figure that has three sides and three angles
- triangle solver and classify triangles
Example calculations for the Triangle Solver and Classify Triangles Calculator
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