Triangle Calculator Degrees Sss

What is the SSS Triangle Method?

The SSS (Side-Side-Side) method is a way to solve for all angles and sides of a triangle when you know the lengths of all three sides. This is one of the three main methods for solving triangles (along with SAS and ASA).

To solve a triangle using the SSS method:

1. First, use the Law of Cosines to find one of the angles
2. Then use the Law of Sines to find another angle
3. The third angle can be found by subtracting the other two angles from 180°
4. Finally, use the Law of Sines again to find the remaining side

How to Use This Calculator

1. Enter the lengths of all three sides of your triangle in the input fields
2. Click the "Calculate" button
3. View the results including all angles and sides
4. Use the chart to visualize the triangle

The calculator will automatically check if the triangle is valid according to the triangle inequality theorem before performing calculations.

Formula and Calculation

The calculator uses these formulas:

Where:

• a, b, c are the lengths of the sides
• A, B, C are the angles opposite to sides a, b, c respectively

The calculation process is:

1. Calculate angle C using the Law of Cosines
2. Calculate angle B using the Law of Sines
3. Calculate angle A as 180° - A - B
4. Calculate side c using the Law of Sines

Worked Example

Let's solve a triangle with sides a=5, b=6, c=7:

1. Calculate angle C:
   cos(C) = (5² + 6² - 7²)/(2×5×6) = (25+36-49)/60 = 12/60 = 0.2 C = arccos(0.2) ≈ 78.46°
2. Calculate angle B:
   sin(B) = (b×sin(C))/c = (6×sin(78.46°))/7 ≈ (6×0.9781)/7 ≈ 0.8396 B ≈ arcsin(0.8396) ≈ 57.22°
3. Calculate angle A:
   A = 180° - 78.46° - 57.22° ≈ 44.32°
4. Calculate side c (already given as 7 in this example)

This example shows how the calculator arrives at the solution for any valid triangle.