Area of Triangle Calculator with Degrees

This calculator helps you find the area of a triangle when you know the lengths of two sides and the angle between them in degrees. The calculation uses trigonometric functions to determine the area accurately.

How to Use This Calculator

To calculate the area of a triangle using two sides and the included angle:

Enter the length of the first side in the "First side" field.
Enter the length of the second side in the "Second side" field.
Enter the included angle in degrees in the "Included angle" field.
Click the "Calculate" button to see the result.

The calculator will display the area of the triangle in square units. You can also view a visual representation of the triangle and its dimensions.

Formula Explained

The area of a triangle can be calculated using two sides and the included angle with the following formula:

Area of Triangle Formula

Area = (1/2) × a × b × sin(C)

Where:

a and b are the lengths of the two sides
C is the included angle in degrees
sin(C) is the sine of angle C

This formula works because the sine function relates the angle to the ratio of the opposite side to the hypotenuse in a right triangle. When applied to any triangle, it gives the height relative to one of the sides.

Worked Examples

Let's look at two examples to see how the formula works in practice.

Example 1: Triangle with sides 5 and 7, angle 45°

Using the formula:

Calculation

Area = (1/2) × 5 × 7 × sin(45°)

sin(45°) ≈ 0.7071

Area ≈ (1/2) × 5 × 7 × 0.7071 ≈ 12.403 square units

Example 2: Triangle with sides 10 and 12, angle 60°

Using the formula:

Calculation

Area = (1/2) × 10 × 12 × sin(60°)

sin(60°) ≈ 0.8660

Area ≈ (1/2) × 10 × 12 × 0.8660 ≈ 51.96 square units

These examples show how the included angle affects the area of the triangle. A larger angle between the sides generally results in a larger area.

Frequently Asked Questions

What units should I use for the sides?: The calculator accepts any length units as long as both sides use the same unit. The result will be in square units (e.g., square meters, square inches).
Can I use this calculator for right triangles?: Yes, you can use this calculator for right triangles. Simply enter 90° as the included angle, and the calculation will work the same as the standard right triangle area formula (1/2 × base × height).
What if I enter an angle greater than 180°?: The calculator will accept angles up to 360°, but angles greater than 180° will produce the same area as their supplementary angle (360° - angle). For example, 210° and 150° will give the same result.
Is there a limit to the size of the numbers I can enter?: The calculator can handle very large numbers, but very large values may cause display or calculation issues due to the limitations of floating-point arithmetic in JavaScript.