triangle is one of the basic geometric shapes that represent the three intersecting line segments.This figure was known scholar of ancient Egypt, ancient Greece and China, which brought most of the formulas and patterns used by scientists, engineers and designers so far.
The main components of the triangle are:
• peak - the point of intersection of the segments.
• Parties - intersecting line segments.
Based on these components, formulate concepts such as perimeter of the triangle, its area, inscribed and circumscribed circles.From school I know that the perimeter of the triangle is a numerical expression of the sum of all three of its sides.At the same time, the formulas for finding this value known to a great many, depending on the source data, which are at a researcher in a particular case.
1. The easiest way to find the perimeter of the triangle is used in the case where the known numerical values of all three of its sides (x, y, z), as a consequence:
P = x + y + z
2. Perimeterequilateral triangle can be found, if we remember that this figure all the parties, however, as all the angles are equal.Knowing the length of this side, the perimeter of an equilateral triangle can be determined by the formula: P =
3x
3. In the isosceles triangle, equilateral unlike only two sides have the same numerical value, however, in this case in the general formperimeter will be as follows:
P = 2x + y
4. The following methods are necessary in cases where the numerical values are not known to all parties.For example, if there is evidence in the investigation of the two sides and the angle between them is known, the perimeter of the triangle can be found by determining the third party and the known angle.In this case, the third party will be found by the formula:
z = 2x + 2y-2xycosβ
Therefore, the perimeter of the triangle is equal to:
P = x + y + 2x + (2y-2xycos β)
5. In the case where the initially given a length of not more than one side of the triangle and the known numerical values of the two angles adjacent thereto, the perimeter of the triangle can be calculated based on the law of sines:
P = x + sinβ x / (sin (180° -β)) + sinγ x / (sin (180 ° -γ))
6. There are cases where to find the perimeter of a triangle using known parameters inscribed in a circle.This formula is also known to most from the school:
P = 2S / r (S - area of a circle, whereas the r - the radius).
From all the above it is clear that the value of the perimeter of the triangle can be found in many ways, on the basis of the data possessed by the researcher.In addition, there are a few special cases, finding this value.Thus, the perimeter is one of the most important values and characteristics of a right triangle.
As you know, this is called a triangle shape, two sides that form a right angle.The perimeter of a right triangle is a numerical expression by the sum of both the legs and the hypotenuse.In the event that a researcher known only data on the two sides, the remainder can be calculated using the famous Pythagorean theorem: z = (x2 + y2), if you know both the leg, or x = (z2 - y2), if we know the hypotenuse and leg.
In that case, if you know the length of the hypotenuse and one of the adjacent corners from her, the other two sides are given by: x = z sinβ, y = z cosβ.In this case, the perimeter of a right triangle is equal to:
P = z (cosβ + sinβ +1)
also a particular case is to calculate the perimeter of a regular (or equilateral) triangle, that is such a figure, in which all sides and all angles are equal.Calculating the perimeter of the triangle on the known side no problem is, however, often the researcher known some other data.So, if you know the radius of the inscribed circle, the perimeter of the triangle is the correct formula:
P = 6√3r
And if given the magnitude of the radius of the circle, the perimeter of the equilateral triangle will be found as follows:
P = 3√3R
FormulaRemember you need to successfully priment in practice.
