Triangle - a geometric figure, which consists of three points in turn they are called vertices, while they are connected in series between the segments.These segments are called sides of the triangle.There are several types of triangles, namely:
1. The magnitude of angles:
- obtuse (when one of the corners of a ninety-degree measure of higher degrees);
- square (where one corner is ninety degrees);
- acute-angled (when all the angles have gradusnuju measure less than ninety degrees).
2. By the number of equal sides:
- diverse (all the parties differ in size);
- isosceles (two sides equal);
- equilateral (all sides have the same length).
worth noting the fact that the sum of the degree measures of angles in a triangle is always 180 degrees, regardless of the type of the figure.So, in the corners of an equilateral triangle, which underlie always equal.In an equilateral triangle, each angle is exactly sixty degrees.In a right triangle to find the angle enough to take away from the known angle of ninety degrees.Then they will know all the steps degree.
Languages degree measure of the angle always gives an answer to the question of how to find the direction of the triangle.Consider all of the examples of a right triangle, as it is more versatile.Besides equilateral and isosceles triangles can be easily represented in the form of two rectangular, but more on that later.
most degree measures are not enough.She needed only to to be able to calculate the trigonometric ratios, namely:
Sin - the ratio of the adjacent leg to the hypotenuse, Cos - the ratio of the opposite leg to the hypotenuse, Tg - the ratio of the adjacent leg to the opposite, Ctg - the ratio of the opposite leg to the adjacent.
So, how to find the side of a right triangle?Knowing the ratio, you can use the sine theorem, which reads as follows: one side belongs to the sine of the angle the same way as the other side is to the sine of the angle of another, and a third party has the same aspect ratio and the sine of the angle as the previous two.
As can be seen from the theorem of sines of knowledge is not enough.We need to know the measure of length has at least one side.Then you find the side of the triangle does not cause too much difficulty.Or there is another option.To locate one of the legs of the triangle must be multiplied by the hypotenuse or the sine of the angle of the adjacent or opposite the cosine.The value of the part does not change.
In addition, you can use all the well-known Pythagorean theorem, which in turn reads the square of the hypotenuse equals the sum of the squares of the other two sides.Here, knowing the two measures of the sides, you can easily determine the value of the third.
There is another theorem on how to find the side of the triangle.Cosine rule: measure the length of the sides is equal to the square root of the sum of the squares of the other two sides without a double product of those parties, which in turn multiplied by the cosine of the angle between them.
But how to find the direction of an isosceles triangle?There are viable all the same principles and theorems, which for a rectangular, but there are some nuances.
First you need to lower the height to the base of the triangle.Thus, we get two identical rectangular triangle, to which we apply the previously studied the possibility.How to find the direction of the triangle?We'll get and the hypotenuse, and two leg.If we find the hypotenuse, then we already know two sides of a triangle.If we have found a leg, which is not high, whereas when multiplying it by two, we obtain a value of a third party.
problem often happens when none of the parties is not given.In this case it is necessary to introduce some unknown X, and continue to search for all parties, not paying attention to the replacement of its kind.
