# How to find the base of a triangle

Often in the problems of planimetry and trigonometry, it is required to find the base of the triangle.

There are even several methods for this operation.

You will need

- Calculator

Instructions

- 1

Strict definition of the concept?The base of the triangle? In geometry does not exist. As a rule, this term denotes the side of a triangle to which a perpendicular is drawn from the opposite vertex (height is omitted). Also this term is usually called? Unequal? Side of an equilateral triangle. Therefore, we choose from the whole variety of examples known in mathematics under the notion of "solution of triangles", variants in which heights and equilateral triangles are encountered.

If the height and area of the triangle are known, thenIn order to find the base of the triangle (the length of the side to which the height is lowered), we use the formula for finding the area of a triangle that states that the area of any triangle can be calculated by multiplying half the length of the base by the length of the height:

S = 1/2 * c * h, where:

S is the area of the triangle,

C is the length of its base,

H is the height of the triangle.

From this formula we find:

C = 2 * S / h.

For example, if the area of the triangle is 20 sq. Cm, and the length of the height is 10 cm, then the base of the triangle will be:

C = 2 * 20/10 = 4 (cm).

- 2

If the side and perimeter of an equilateral triangle are known, then the length of the base can be calculated by the following formula:

C = P-2 * a, where:

P is the perimeter of the triangle,

A is the length of the lateral side of the triangle,

C is the length of its base.

- 3

If the side and the opposite of the angle of an equilateral triangle are known, then the length of the base can be calculated by the following formula:

C = a *? (2 * (1-cosC)), where:

C is the value of the angle of an equilateral triangle opposite to the base,

A is the length of the lateral side of the triangle.

C is the length of its base.

(The formula is a direct consequence of the cosine theorem)

There is also a more compact record of this formula:

C = 2 * a * sin (B / 2)

- 4

If the lateral side and the value of the angle of an equilateral triangle adjacent to the base are known, then the length of the base can be calculated from the following easily remembered formula:

C = 2 * a * cosA

A is the value of the angle of an equilateral triangle adjacent to the base,

A is the length of the lateral side of the triangle.

C is the length of its base.

This formula is a consequence of the projection theorem.

- 5

If the radius of the circumscribed circle and the value of the angle of an equilateral triangle opposite to the base are known, then the length of the base can be calculated by the following formula:

C = 2 * R * sinC, where:

C is the value of the angle of an equilateral triangle opposite to the base,

R is the radius of a circle circumscribed around a triangle,

C is the length of its base.

This formula is a direct consequence of the sine theorem.