Triangle Calculator with Degrees

This triangle calculator helps you determine the properties of a triangle when you know some of its sides and angles in degrees. Whether you're solving for missing sides, angles, or area, this tool provides accurate calculations based on standard trigonometric principles.

How to Use This Calculator

To use the triangle calculator with degrees, follow these steps:

Select the type of triangle you're working with (scalene, isosceles, or equilateral).
Enter the known values for sides and angles in degrees.
Click "Calculate" to see the results.
Review the calculated values and chart visualization.
Use the "Reset" button to clear all inputs and start over.

The calculator will automatically determine which values to solve for based on the inputs you provide. For example, if you enter two sides and one angle, it will calculate the remaining side and angles.

Formulas Used

The triangle calculator uses several fundamental trigonometric formulas to solve for unknown values:

Law of Sines

a / sin(A) = b / sin(B) = c / sin(C)

Where a, b, c are the lengths of the sides opposite angles A, B, C respectively.

Law of Cosines

c² = a² + b² - 2ab cos(C)

Where c is the side opposite angle C, and a and b are the other two sides.

Area of a Triangle

Area = (1/2) * a * b * sin(C)

Where a and b are two sides, and C is the included angle.

The calculator automatically selects the appropriate formula based on which values you provide. For example, if you know two sides and the included angle, it will use the area formula directly.

Worked Examples

Let's look at a practical example to see how the calculator works.

Example 1: Solving for Missing Side

Given a triangle with sides a = 5, b = 7, and angle C = 60°, find side c.

Using the Law of Cosines:

c² = 5² + 7² - 2 * 5 * 7 * cos(60°)

c² = 25 + 49 - 70 * 0.5

c² = 74 - 35 = 39

c = √39 ≈ 6.245

Example 2: Solving for Missing Angle

Given a triangle with sides a = 8, b = 5, and angle A = 30°, find angle B.

Using the Law of Sines:

a / sin(A) = b / sin(B)

8 / sin(30°) = 5 / sin(B)

8 / 0.5 = 5 / sin(B)

16 = 5 / sin(B)

sin(B) = 5 / 16 ≈ 0.3125

B ≈ arcsin(0.3125) ≈ 18.435°

These examples demonstrate how the calculator applies trigonometric principles to solve for unknown values in a triangle.

Frequently Asked Questions

What types of triangles can this calculator solve?

This calculator can solve for any type of triangle: scalene (all sides and angles different), isosceles (two sides and two angles equal), and equilateral (all sides and angles equal).

How accurate are the calculations?

The calculations use standard trigonometric formulas and are accurate to several decimal places. The results are displayed with appropriate precision for practical use.

Can I use this calculator for right triangles?

Yes, you can use this calculator for right triangles. Simply set one angle to 90° and provide the other known values to get the remaining sides and angles.

What if I don't know any angles?

If you only know the lengths of all three sides, the calculator will use the Law of Cosines to determine the angles. If you know two sides and the included angle, it will calculate the other sides and angles.