# How to calculate the direction of an isosceles triangle

Isosceles or an equilateral triangle is called, in which the lengths of two sides of the same. If you want to calculate the length of one side of the figure, you can use the knowledge of the values of angles in the vertices in combination with the length of one side or the radius of the circumscribed circle. These parameters polygon linked theorems of sine, cosine and some other permanent relationships.

## Instruction how to calculate the direction of an isosceles triangle

Step 1:

To calculate the side length of the isosceles triangle (b) under conditions known in the length of the base (a) and the size of the adjacent angle (α) using the cosine theorem. From this it follows that you should divide the length of the well-known side to twice the cosine of the given angle in a: b = a / (2 * cos (α)).

Step 2:

The same theory is applied to the reverse operation and - calculating the base length (a) on the side of the known length (b) and the magnitude of the angle (α) between the two sides. In this case, the theorem enables us to obtain equality, the right part of which contains twice the product of the length of the well-known side to the cosine of the angle: a = 2 * b * cos (α).

Step 3:

If the lengths of the sides other than (b) in a given value of the angle between them (β), to calculate the length of the base (a) use the sine theorem. It follows from the formula, according to which should be twice the side length multiplied by the sine of half the known angle: a = 2 * b * sin (β / 2).

Step 4:

The theorem of sines can be used to find the length of the side (b) of an isosceles triangle, if we know the length of the base (a) and the value of his opposing angle (β). In this case, double the sine of half the known angle and divide the resulting value of the base length: b = a / (2 * sin (β / 2)).

Step 5:

If nearly isosceles triangle described by a circle with a radius (R) is known, to calculate the lengths of the sides need to know the angle at one of the vertices of the figure. If the conditions for information about the angle between the sides (β), Calculate the length of the base (a) the product range of the polygon doubling the value of the sine of the angle: a = 2 * R * sin (β). If the angle is given to the base (α), to find the side length (b), simply replace the angle in this formula: b = 2 * R * sin (α).