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Guide
1
rigorous definition of "base Triangle" in geometry does not exist.As a rule, this term means, side of the triangle to which of the opposing peaks held perpendicular (lowered height).Also, this term is called "unequal" side of an equilateral triangle.Therefore, choose from the variety of examples, known in mathematics, the term "solution triangle" options that meet height and equilateral triangles.
If you know the height and area of ​​the triangle, in order to find the base of the triangle (side length, which lowered the height), use the formula of finding the area of ​​a triangle, which states that the area of ​​any triangle can be calculated by multiplying half the length of the base of the length of the altitude:
S= 1/2 * c * h, where:
S - area of ​​the triangle,

with - the length of its base,

h - the height of the length of the triangle.
From this formula we find:
c = 2 * S / h.
For example, if the area of ​​the triangle is equal to 20 square centimeters, and the length of height - 10 cm, the base of the triangle is:
c = 2 * 20/10 = 4 (cm).
2
If you know the side and the perimeter of an equilateral triangle, the length of the base can be calculated using the following formula:
c = P 2 * a, where:
P - perimeter of the triangle,

and - the length of the sideside of the triangle,

with - the length of its base.
3
If you know the side and the value opposite the base angles of an equilateral triangle, the length of the base can be calculated using the following formula:
c = a * √ (2 * (1-cosC)), where:
C- the value of the opposite bottom corner of an equilateral triangle,

a - side length of the triangle.

with - the length of its base.
(The formula is a direct consequence of the theorem of cosines)
There is also a more compact notation this formula:
c = 2 * a * sin (B / 2)
4
If you know the side and the value of adjacent base angle of an equilateralthe triangle, the length of the base can be calculated using the following easy to remember formula:
c = 2 * a * cosA
A - value of the adjacent base angle of an equilateral triangle,

and - the length of the side of the triangle.

with - the length of its base.
This formula is a consequence of the theorem on projections.
5
If the known radius of the circumscribed circle and the magnitude of the opposite bottom corner of an equilateral triangle, the base length can be calculated using the following formula:
c = 2 * R * sinC, wherein:
C - the magnitude of the opposite bottom corner of an equilateraltriangle,

R - the radius of the circle around the triangle,

with - the length of its base.
This formula is a direct consequence of the theorem of sines.