Kilometer Tangent to Area Calculation

How to Use This Calculator

1. Enter the length of the first side of the triangle in kilometers.
2. Enter the length of the second side of the triangle in kilometers.
3. Enter the measure of the angle between these two sides in radians.
4. Click the "Calculate" button to compute the area.
5. The area of the triangle will be displayed in square kilometers.

Principle of Calculation

This calculator uses the formula for the area of a triangle when two sides and the included angle are known:

Area = 0.5 × side1 × side2 × sin(angle)

This formula works because the area of a triangle can be thought of as half the product of the base and height. When you know two sides and the included angle, you can determine the height using trigonometry, and then use the standard area formula.

Example

Suppose you have a triangle with sides of 5 km and 7 km, and the angle between them is 1.2 radians. The area would be:

Area = 0.5 × 5 × 7 × sin(1.2) ≈ 14.9494 km²

Notes

• Make sure all measurements are in the same units (in this case, kilometers).
• The angle must be in radians, not degrees.
• This formula works for any triangle, regardless of its shape (acute, obtuse, or right triangle).