Triangle Area Calculator with Degrees

Calculate the area of a triangle when you know two sides and the included angle in degrees. This calculator uses the basic trigonometric formula for triangle area calculation.

How to Use This Calculator

To calculate the area of a triangle using degrees:

Enter the length of the first side in the "Side A" field
Enter the length of the second side in the "Side B" field
Enter the included angle in degrees in the "Angle" field
Click the "Calculate" button

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

Formula Explained

The area of a triangle can be calculated using the formula:

Area = (Side A × Side B × sin(Angle)) / 2

Where:

Side A is the length of the first side
Side B is the length of the second side
Angle is the included angle between the two sides in degrees

The sine function (sin) converts the angle from degrees to a ratio that can be used in the area calculation.

Practical Examples

Example 1: Right Triangle

For a right triangle with sides of 3 units and 4 units, and a 90° angle between them:

Area = (3 × 4 × sin(90°)) / 2 = (12 × 1) / 2 = 6 square units

Example 2: Obtuse Triangle

For a triangle with sides of 5 units and 7 units, and a 120° angle between them:

Area = (5 × 7 × sin(120°)) / 2 ≈ (35 × 0.866) / 2 ≈ 15.15 square units

Example 3: Acute Triangle

For a triangle with sides of 6 units and 8 units, and a 30° angle between them:

Area = (6 × 8 × sin(30°)) / 2 = (48 × 0.5) / 2 = 12 square units

Frequently Asked Questions

What units should I use for the sides?: The calculator accepts any length units, but the result will be in the square of those units. For example, if you enter sides in meters, the area will be in square meters.
Can I calculate the area of any triangle with this calculator?: Yes, this calculator works for any triangle where you know two sides and the included angle. It's particularly useful for non-right triangles.
What if I don't know the angle between the sides?: If you don't know the included angle, you would need to use a different method, such as Heron's formula, which requires all three sides of the triangle.
Is the result always accurate?: The calculator uses standard trigonometric functions and provides precise results based on the inputs you provide. However, ensure your measurements are accurate for reliable results.
Can I use this calculator for large triangles?: Yes, the calculator can handle any size triangle as long as the inputs are within the limits of standard floating-point arithmetic in JavaScript.