Isosceles, or ravnoboky call a triangle at which lengths of two parties are identical. In need of calculation of length of one of the parties of such figure it is possible to use knowledge of sizes of corners in its tops in combination with length of one of the parties or radius of a circumscribed circle. These parameters of a polygon are connected among themselves by theorems of sine, cosines and some other constant ratios.
Instruction
1. For calculation of length of side of an isosceles triangle (b) on length of the basis (a), known from conditions, and size of the corner adjoining to it (α) use the theorem of cosines. From it follows that you should divide length of the known party into the doubled cosine of the corner given in conditions: b = a/(2*cos(α)).
2. Apply the same theorem also to the return operation - calculation of length of the basis (a) on the known length of side (b) and size of a corner (α) between these two parties. In this case the theorem allows to receive equality which right part contains the doubled work of length of the known party on a cosine of the angle: a = 2*b*cos(α).
3. If except lengths of sides (b) the corner size between them is specified in conditions (β), for calculation of length of the basis (a) use the theorem of sine. From it the formula according to which it is necessary to increase the doubled length of side by a sine of a half of the known corner follows: a = 2*b*sin (β/2).
4. The theorem of sine can be used also for finding of length of side (b) of an isosceles triangle if length of the basis (a) and size opposite is known to it a corner (β). In this case double a sine of a half of the known corner and divide basis length into the turned-out value: b = a/(2*sin(β/2)).
5. If about an isosceles triangle the circle which radius (R) is known is described, for calculation of lengths of the parties it is necessary to know corner size in one of figure tops. If information on coal between sides is provided in conditions (β), calculate length of the basis (a) of a polygon doubling of the work of radius on value of a sine of this corner: a = 2*R*sin(β). If corner size at the basis is given (α), for finding of length of side (b) just replace a corner in this formula: b = 2*R*sin(α).