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 3 Using Law of Cosines:
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 = | 482 + 552 - 732 |
| 2 * 48 * 55 |
| Angle 3 = | 2304 + 3025 - 5329 |
| 5280 |
| Angle 3 = | 0 |
| 5280 |
Angle 3 = Arccos(0)
Angle 3 = 90°
Find Angle 2 Using Law of Cosines
Take Arccosine of the following:| Angle 2 = | Side 12 + Side 32 - Side 22 |
| 2 * Side 1 * Side 3 |
| Angle 2 = | 482 + 732 - 552 |
| 2 * 48 * 73 |
| Angle 2 = | 2304 + 5329 - 3025 |
| 7008 |
| Angle 2 = | 4608 |
| 7008 |
Angle 2 = Arccos(0.65753424657534)
Angle 2 = 48.888°
Now solve for Angle 1
The sum of angles n a triangle = 180
Missing Angle = 180 - sum of 2 angles
Angle 1 = 180 - (Angle2 + Angle 3)
Angle 1 = 180 - (48.887909560833 + 90)
Angle 1 = 180 - 138.88790956083
Angle 1 = 41.112°
Calculate Semi-Permieter (s)
Use Heron's formula| s = | Side1 + Side2 + Side3 |
| 2 |
| s = | 48 + 55 + 73 |
| 2 |
| s = | 176 |
| 2 |
s = 88
Calculate Area (A)
Use Heron's formulaA = √s * (s - side1) * (s - side2) * (s - side3)
A = √88 * (88 - 48) * (88 - 55) * (88 - 73)
A = √88 * (40) * (33) * (15)
A = √1742400
A = 1320
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
Common Core State Standards In This Lesson
HSG.CO.B.8, HSG.SRT.D.10, HSG.SRT.D.11
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
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
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
