How to find the side of the triangle. Starting with a simple

A triangle is a geometric figure that consists of three points, in turn they are called vertices, while they are joined together in succession by segments. Such segments are called the sides of a triangle. There are several types of triangles, namely:

1. From the angles:

- obtuse (when one of the corners has a degree measure above ninety degrees);

- rectangular (when one of the corners has ninety degrees);

- acute-angled (when all angles have a degree measure less than ninety degrees).

2. By number of equal parties:

- versatile (all sides differ in magnitude);

- isosceles (two sides are equal to each other);

- Equilateral (all sides have the same length).

It should be noted that the sum of degree angles in a triangle is always 180 degrees, regardless of the type of the figure itself. Thus, in an isosceles triangle, the angles that lie in the base are always equal. And in an equilateral triangle, each corner has exactly sixty degrees. In a right-angled triangle, to find the angle, it is sufficient to subtract a known angle from ninety degrees. Then all the graded measures will be known.

Knowing the degree measure of the angle will always give an answer to the question of how to find the side of the triangle. Consider all the examples of a right triangle, since it is more universal. In addition, an equilateral and isosceles triangle can easily be represented as two rectangular triangles, but this is a little later.

The most gradual measure is not enough. It is needed only in order that it is possible to calculate trigonometric relations, namely:

Sin is the ratio of the adjacent leg to the hypotenuse, Cos is the ratio of the opposite leg to the hypotenuse, Tg is the ratio of the adjacent leg to the opposite, and Ctg is the ratio of the opposite leg to the adjacent one.

So, how to find the side of a right triangle? Knowing the relationships, one can use the sine theorem, which says: one side refers to the sine of the angle, just as the other side refers to the sine of the other corner, and the third side has the same side-sine relation of the angle as the two previous ones.

As you can see from the theorem, one knowledge of sines is not enough. It is necessary to know the measure of the length of at least one other side. Then how to find the side of the triangle will not cause any more difficulties. Or another option is possible. To find one of the triangle's legs, it is necessary to multiply the hypotenuse either by the sine of the adjacent angle, or by the cosine of the opposite corner. The side value will not change.

In addition, we can use the well-known theorem of Pythagoras, which in turn says: the square of the hypotenuse is equal to the sum of the squares of the legs. Here, knowing the two measures of the parties, you can easily determine the value of the third.

There is another theorem on how to find the side of a triangle. The cosine theorem: the measure of the length of a side is equal to the square root of the sum of squares of the other two sides without the double product of these sides, which in turn multiply by the cosine of the angle between them.

And how to find the side of an isosceles triangle? Here all the same principles and theorems have the right to exist, as for a rectangular one, but there are several nuances.

First, you need to lower the height to the base of the triangle. Thus, we get two identical rectangular triangles, to which we will apply the previously studied possibilities. How to find the side of the triangle? We will get both a hypotenuse and two legs. If we find the hypotenuse, then we already know the two sides of the triangle. If we find a catheth that is not a height, then multiplying it by two, we get the value of the third party.

Often, there are tasks when neither side is specified. In this case, it is necessary to introduce some unknown X, and continue the search for all parties, not paying attention to the replacement of this kind.