Advice 1: How to find centroid of a triangle

The triangle is one of the basic geometric shapes. And only he has the "wonderful" points. These include, for example, the center of gravity point, which accounts for the weight of the entire figure. Where is this wonderful spot and how to find it?
How to find centroid of a triangle
You will need
  • pencil, ruler
Instruction
1
Draw the triangle. To do this, take a ruler and draw a pencil line. Then, draw another segment starting from one end previous. Close the figure by connecting the two remaining free points of the segments. Get the triangle. It was his center of gravity should look for.
2
Take a ruler and measure the length of one side. Find the middle of that side and mark it with a pencil. Spend the cut from the opposite vertex to the target point. The resulting segment is called a median.
3
Let's get to the other side. Measure its length, divide into two equal parts and draw a midpoint of the opposite lying vertex.
4
Do the same with a third party. Please note that if you did everything correctly, then the medians will intersect at one point. This will be the center of gravity or, as it is called, the center of mass of the triangle.
5
If your goal is to find the center of gravity of the equilateral triangle, then draw a height from each vertex of the figure. To do this, take a ruler with a right angle and one side, leaning against the base of the triangle, and the second point to the opposite vertex. Do the same with other parties. The point of intersection will be the centerom of gravity. Feature of equilateral triangles is that the same segments are the medians, and altitudes, and bisectors.
6
The center of gravity of any triangle divides the medians into two segments. Their ratio is 2:1, when viewed from the top. If the triangle is placed on the pin so that the centerof OID will be at its edge, he will not fall, and will be in equilibrium. Also the center of gravity is the point which represents the whole mass placed at the vertices of the triangle. Repeat this experience and make sure that this point is a reason is called "wonderful".
Note
Jobs can be specified that it is necessary to find the center of gravity, center of mass or centroid. All three names refer to the same thing.

Advice 2 : How to find the length of sides of isosceles triangle

Isosceles is a triangle in which the lengths of two sides are the same. To calculate the size of any of the parties need to know the length of the other sides and one angle or radius of the triangle circumscribed around the circle. According to the known values for calculations it is necessary to use the formulas derived from theorems of sine or cosine, or from the theorem on projections.
How to find the length of sides of isosceles triangle
Instruction
1
If you know the length of base of isosceles triangle (A) and the value adjacent to it angle (angle between the base and any lateral face) (α), then calculate the length of each of the sides (B) based on the spherical law of cosines. It will be equal to the private from dividing the length of the base to twice the value of the cosine of the known angle B=A/(2*cos(α)).
2
The length of the sides of an isosceles triangle, which is its base (A) can be calculated on the basis of the same cosines, if you know the length of its lateral side (B) and the angle between it and the base (α). It will be equal to twice the product of the known sides into the cosine of the known angle A=2*B*cos(α).
3
Another way to find the length of the base of an isosceles triangle can be used if we know the value of him opposite the angle (β) and the length of the lateral side (B) of the triangle. It will be equal to twice the product of length of the lateral sides by the sine of half the value of the known angle A=2*B*sin(β /2).
4
Similarly, we can deduce the calculation formula of lateral sides of the isosceles triangle. If the known base length (A) and the angle between the equal sides (β), the length of each (B) will be equal to the result of dividing the base length to twice the sine of half the value of the known angle B=A/(2*sin(β /2)).
5
If you know the radius described around an isosceles triangle on the circle (R), then the lengths of its sides can be calculated, knowing the value of one of the corners. If we know the value of the angle between the sides (β), the length of the partiesconstituting the grounds (A), is equal to twice the product of the radius of the circumscribed circle by the sine of this angle A=2*R*sin(β).
6
If you know the radius of the circumscribed circle (R) and the angle adjacent to the base (α), the length of the lateral side (B) will be equal to twice the product of the base length by the sine of the known angle B=2*R*sin(α).
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