Rhombus it is possible to call a parallelogram which diagonals halve the corners lying in figure tops. Except this property of diagonal of a rhombus are remarkable the fact that are axes of symmetry of a polygon, are crossed only at right angle, and the only general point divides each of them into two equal pieces. These properties allow to calculate easily length of one of diagonals if length another and still some parameter of a figure - the size of the party, a corner in one of tops is known, the area, etc.
Instruction
1. If except length of one of diagonals (l) the considered quadrangle is known that it is a special case of a rhombus - a square, it is not necessary to make any calculations. In this case lengths of both diagonals are identical - just equate required size (L) to known: L=l.
2. Knowledge of length of the party of a rhombus (a) in addition to length of one of diagonals (l) will allow to calculate length of another (L) in Pythagorean theorems. It is possible because two half of the crossed diagonals form a rectangular triangle with the party of a rhombus. Half of diagonals in it are legs, and the party - a hypotenuse therefore the equality following from Pythagorean theorem can be written down so: a² = (l/2)² + (L/2)². For use in calculations transform it to such look: L = √ (4*a²-l²).
3. At the known size of one of corners (α) of a rhombus and length of one of diagonals (l) for finding of size of another (L) consider the same rectangular triangle. The tangent of a half of the known corner will be equal in it to the relation of length of an opposite leg - half of diagonal of l - to adjacent - a half of diagonal of L: tg(α/2) = (l/2)/(L/2) = l/L. Therefore for calculation of required size use formula L = l/tg(α/2).
4. If length of perimeter (P) of a rhombus and the size of its diagonal (l) is specified in statements of the problem, the formula of calculation of length of the second (L) can be reduced to the equality used in the second step. For this purpose divide perimeter into the four and replace with this expression length of the party in a formula: L = √ (4*(P/4)²-l²) = √ (P²/4-l²).
5. The area (S) of a figure also can be specified in initial conditions except length of one of diagonals (l). Then for calculation of length of the second diagonal of a rhombus (L) use very simple algorithm - double the area and divide the received value into length of the known diagonal: L = 2*S/l.