Geometry - Science is not simple. It can come in handy both for a school program and in real life. Knowledge of many formulas and theorems will simplify geometric calculations. One of the most simple figures in geometry is a triangle. One of the varieties of triangles, equilateral, has its own characteristics.
Features of the equilateral triangle
According to the definition, the triangle is a polyhedron who has three angle and three sides. This is a flat two-dimensional figure, its properties are studied in high school. By the type of angle distinguish with acute-angular, stupid and rectangular triangles. The rectangular triangle is such a geometric figure, where one of the corners is 90º. Such a triangle has two categories (they create a straight corner), and one hypotenuse (it is opposite the direct angle). Depending on which values \u200b\u200bare known, there are three simple methods to calculate the hypothen of the rectangular triangle.
The first way to find the hypothen of the rectangular triangle is. Pythagorean theorem
Pythagora theorem is an oldest way to calculate any of the sides of the rectangular triangle. It sounds like this: "In a rectangular triangle, the square of hypotenuse is equal to the sum of the squares of the cathets." Thus, to calculate the hypotenuse, you should withdraw the square root of two cathets in the square. For clarity, formulas and scheme are given.
The second way. Calculation of hypotenuses with 2 known quantities: Cate and adjacent angle
One of the properties of the rectangular triangle states that the ratio of the length of the catech to the length of the hypotenuse, is equivalent to the cosine of the angle between the etiv or hypotenuse. We call the corner-known angle α. Now, due to known definition, it is easy to formulate a formula for calculating hypotenuses: hypotenuse \u003d catat / COS (α)
Third way. Calculation of hypotenuse with 2 known values: Cate and an opposite corner
If the opposite angle is known, it is possible to take advantage of the properties of the rectangular triangle again. The ratio of the length of the catech and hypotenuse is equivalent to the sinus of an opposing corner. Again we call the known angle α. Now for calculations we apply a little different formula:
Hypotenuse \u003d catat / sin (α)
Examples that will help deal with formulas
For a deeper understanding of each of the formulas, visual examples should be considered. So, suppose there is a rectangular triangle, where there are such data:
- Catat - 8 cm.
- The adjacent angle cosα1 - 0.8.
- The opposite angle of SINα2 - 0.8.
According to Pythagore: hypotenuse \u003d square root of (36 + 64) \u003d 10 cm.
By the magnitude of the category and adjacent angle: 8 / 0.8 \u003d 10 cm.
The magnitude of the category and the opposite angle: 8 / 0.8 \u003d 10 cm.
Observing in the formula, it is possible to easily calculate the hypotenuse with any data.
Video: Pythagore's theorem
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