Triangle Calculator Degrees

This triangle calculator helps you find all angles of a triangle when you know at least two sides and one angle, or when you know all three sides. The calculator works in degrees and provides a visual representation of the triangle.

How to Use This Calculator

To use the triangle calculator, follow these steps:

Enter the lengths of the three sides of the triangle in the input fields labeled "Side a", "Side b", and "Side c".
Alternatively, you can enter two sides and one angle to calculate the remaining sides and angles.
Click the "Calculate" button to compute the angles and other properties of the triangle.
Review the results displayed in the result panel, including the angles in degrees.
Use the chart to visualize the triangle's angles.

Note: The calculator assumes the triangle is valid based on the triangle inequality theorem. If the sides do not form a valid triangle, the calculator will display an error message.

Formulas Used

The triangle calculator uses the following formulas to calculate the angles:

Angle A = arccos((b² + c² - a²) / (2bc)) * (180/π) Angle B = arccos((a² + c² - b²) / (2ac)) * (180/π) Angle C = 180° - Angle A - Angle B

Where:

a, b, c are the lengths of the sides of the triangle
arccos is the inverse cosine function
π is the mathematical constant pi (approximately 3.14159)

The calculator converts the angles from radians to degrees by multiplying by (180/π).

Worked Examples

Example 1: Equilateral Triangle

Given a triangle with sides a = 5, b = 5, c = 5:

Using the formula:

Angle A = arccos((5² + 5² - 5²) / (2 * 5 * 5)) * (180/π) Angle A = arccos((25 + 25 - 25) / 50) * (180/π) Angle A = arccos(25/50) * (180/π) Angle A = arccos(0.5) * (180/π) Angle A = 60°

Similarly, Angle B and Angle C will also be 60°.

Example 2: Right-Angled Triangle

Given a triangle with sides a = 3, b = 4, c = 5:

Using the formula:

Angle A = arccos((4² + 5² - 3²) / (2 * 4 * 5)) * (180/π) Angle A = arccos((16 + 25 - 9) / 40) * (180/π) Angle A = arccos(32/40) * (180/π) Angle A = arccos(0.8) * (180/π) Angle A ≈ 36.87° Angle B = arccos((3² + 5² - 4²) / (2 * 3 * 5)) * (180/π) Angle B = arccos((9 + 25 - 16) / 30) * (180/π) Angle B = arccos(18/30) * (180/π) Angle B = arccos(0.6) * (180/π) Angle B ≈ 53.13° Angle C = 180° - 36.87° - 53.13° ≈ 90°

Frequently Asked Questions

What is a triangle calculator?: A triangle calculator is a tool that helps you calculate various properties of a triangle, including its angles, when you know some of its sides or angles.
How do I use the triangle calculator?: Enter the lengths of the sides of the triangle in the input fields and click the "Calculate" button. The calculator will display the angles of the triangle in degrees.
What formulas does the triangle calculator use?: The calculator uses the Law of Cosines to calculate the angles of the triangle based on the lengths of its sides.
Can the triangle calculator handle right-angled triangles?: Yes, the calculator can handle right-angled triangles as well as other types of triangles.
What if the sides I enter do not form a valid triangle?: The calculator will display an error message if the sides do not form a valid triangle according to the triangle inequality theorem.