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The area of a triangle across two sides and the angle between them.

Зная две стороны треугольника и угол между ними, можно вычислить его площадь.

The online calculator below allows you to find:
- The area of a triangle through two sides and the angle between them;
- The side of the triangle through the area of the triangle, the other side and the angle between them; - The angle between the sides of a triangle through its area and sides.

The area of a triangle is one of the main parameters that determine its shape. There are several ways to calculate the area of a triangle, including using two of its sides and the angle between them.

The formula for calculating the area of a triangle in terms of its two sides and the angle between them is called the sine formula. It looks like this: S = (1/2) * a * b * sin(α), where S is the area of the triangle, a and b are the lengths of two sides, α is the angle between these sides.

To understand how this formula works, let's look at an example. Suppose we have a triangle with sides of length 5 and 7, and an angle between them of 60 degrees. To calculate the area of this triangle, we can use the sine formula. First we calculate the sine of angle α: sin(α) = sin(60) = √3/2. Then we plug the sides and angle into the formula: S = (1/2) * 5 * 7 * √3/2 = 10.61. Thus, the area of a triangle is 10.61 square units.

The sine formula allows you to calculate the area of a triangle if you know the lengths of its two sides and the angle between them. It is based on the properties of the sine, which relates the ratio of the length of a side and the opposite angle in a triangle. This formula can be useful for solving problems in geometry, mechanics, physics and other fields of science.

It's important to note that the sine formula is not the only way to calculate the area of a triangle. There are other formulas, for example, Heron's formula, which calculates the area of a triangle in terms of the lengths of all its sides. However, the sine formula can be useful in cases where only two sides and the angle between them are known.

In conclusion, the sine formula allows you to calculate the area of a triangle in terms of its two sides and the angle between them. It is based on the properties of the sine and can be used to solve problems in geometry, mechanics, physics and other fields of science.
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