Triangle Area Calculator 2 Sides 1 Angle Square Root

This triangle area calculator helps you find the area of a triangle when you know two sides and the included angle. The calculation uses the formula involving the square root of the product of the two sides.

How to Use This Calculator

To calculate the area of a triangle using two sides and one 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.
Use the "Reset" button to clear all fields and start over.

The calculator will display the area of the triangle in square units. You can also view a chart showing the relationship between the sides and angle.

The Formula Explained

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

Area = (1/2) × a × b × sin(θ)

Where:

a is the length of the first side
b is the length of the second side
θ is the included angle in degrees

The formula uses the sine of the included angle to calculate the height of the triangle, then multiplies by the base (one of the sides) to get the area.

Important Notes

Make sure the angle you enter is the included angle between the two sides. The calculator will convert the angle from degrees to radians for the sine calculation.

Worked Example

Let's calculate the area of a triangle with sides of 5 units and 7 units, and an included angle of 30 degrees.

Convert the angle to radians: 30° × (π/180) ≈ 0.5236 radians
Calculate the sine of the angle: sin(0.5236) ≈ 0.5
Multiply the sides and sine: 5 × 7 × 0.5 = 17.5
Multiply by 1/2: 17.5 × 0.5 = 8.75

The area of the triangle is 8.75 square units.

Frequently Asked Questions

What is the included angle in a triangle?

The included angle is the angle between the two sides you know. It's the angle that connects the two sides when you draw the triangle.

Can I use this calculator for any type of triangle?

Yes, this calculator works for any triangle as long as you know two sides and the included angle. It doesn't matter if the triangle is acute, right, or obtuse.

What if I don't know the included angle?

If you don't know the included angle, you'll need to use a different method to find the area, such as Heron's formula, which requires all three sides of the triangle.