Find The Degrees of A Triangle Calculator

Triangles are fundamental shapes in geometry with three sides and three angles that always add up to 180 degrees. This calculator helps you determine the degrees of each angle in a triangle when you know the lengths of all three sides. Understanding how to find the degrees of a triangle is essential for geometry problems, construction, and various scientific applications.

How to Use the Calculator

Using our triangle degrees calculator is simple. Follow these steps to find the angles of your triangle:

Enter the length of side A in the first input field.
Enter the length of side B in the second input field.
Enter the length of side C in the third input field.
Click the "Calculate" button to compute the angles.
Review the results displayed below the calculator.

The calculator will display the degrees for each angle (A, B, and C) of the triangle based on the side lengths you provided. The results are presented in a clear format with the angle values and a visual representation of the triangle.

Formula Explained

To find the degrees of a triangle when you know the lengths of all three sides, we use the Law of Cosines. The formula for each angle is:

Angle A = cos⁻¹((b² + c² - a²) / (2bc)) Angle B = cos⁻¹((a² + c² - b²) / (2ac)) Angle C = cos⁻¹((a² + b² - c²) / (2ab))

Where:

a, b, and c are the lengths of the sides opposite angles A, B, and C respectively.
cos⁻¹ is the inverse cosine function, which returns the angle in degrees.

This formula allows us to calculate each angle of the triangle using the side lengths. The calculator applies this formula to provide accurate results for your specific triangle.

Worked Examples

Let's look at a practical example to understand how the calculator works. Suppose we have a triangle with sides:

Side A = 5 units
Side B = 6 units
Side C = 7 units

Using the formula:

Angle A = cos⁻¹((6² + 7² - 5²) / (2 * 6 * 7)) = cos⁻¹((36 + 49 - 25) / 84) = cos⁻¹(60/84) ≈ 36.87° Angle B = cos⁻¹((5² + 7² - 6²) / (2 * 5 * 7)) = cos⁻¹((25 + 49 - 36) / 70) = cos⁻¹(38/70) ≈ 49.13° Angle C = cos⁻¹((5² + 6² - 7²) / (2 * 5 * 6)) = cos⁻¹((25 + 36 - 49) / 60) = cos⁻¹(12/60) ≈ 94.00°

The calculator would display these angle values for the given side lengths. This example demonstrates how the calculator applies the Law of Cosines to find the degrees of each angle in a triangle.

Frequently Asked Questions

What is the sum of the angles in a triangle?

The sum of the interior angles in any triangle is always 180 degrees. This is a fundamental property of triangles in Euclidean geometry.

Can I use this calculator for any type of triangle?

Yes, this calculator can be used for any triangle as long as you know the lengths of all three sides. It works for scalene, isosceles, and equilateral triangles.

What if I only know two sides and an angle?

If you know two sides and an angle, you can use the Law of Sines to find the other angles and sides. Our calculator is specifically designed for cases where all three sides are known.