Often on the plane geometry and trigonometry problems need to find the base of the triangle.

For this operation, there are even several methods.

You will need

• Calculator

instructions

1

A rigorous definition of the concept?the base of the triangle? geometry exists. As a rule, this term denotes, side of the triangle to which the vertices of the opposite held perpendicular (lowered height). Also, this term is called? Unequal? side of an equilateral triangle. So choose from the variety of examples, known in mathematics, the term? Solution ?, triangles options that include the height and equilateral triangles.
If you know the height and area of ​​the triangle, theto find the base of the triangle (side length, the height of which is omitted), we 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 base length by the height of the length:
S = 1/2 * c * h, where:
S - area of ​​the triangle,

c - the length of a base

h - the height of the triangle length.
From this formula, we find:
c = 2 * S / h.
For example, if the area of ​​the triangle is equal to 20 square centimeters, and a height of length - 10 cm, the base of the triangle is:
c = 2 * 20/10 = 4 (cm).

2

If the known side and perimeter of an equilateral triangle, the base length can be calculated using the following formula:
with P = 2 * a where:
P - perimeter of the triangle,

and - the length of the side of the triangle,

c - the length of a base.

3

If the known value and the side opposite the base angles of an equilateral triangle, the base length can be calculated using the following formula:
c = a * (2 * (1-cosC)), where:
C - the value of the base of the opposite corner of an equilateral triangle,

and - the length of the lateral sides of the triangle.

c - the length of a base.
(The formula is the 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 the adjacent base angle of an equilateral triangle, the base length can be calculated using the following easy to remember formula:
c = 2 * a * COSA
A - the value of the adjacent base angle of an equilateral triangle,

and - the length of the lateral sides of the triangle.

c - the length of a 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 value of the base of the opposite corner of an equilateral triangle,

R - radius of the circle circumscribed around the triangle,

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