At the rhomb side are equal and pairwise parallel. Its diagonals intersect at a right angle and divide the point of intersection into equal parts.
These properties easily allow us to find the value of the diagonals of the rhombus.
Denote the vertices of the rhombus in Latin lettersAlphabet A, B, C and D for convenience of discussion. The point of intersection of diagonals is traditionally denoted by the letter O. The length of the rhombus's edge is denoted by the letter a. The value of the angle BCD, which is equal to the angle BAD, is denoted by α-.
Let us find the value of the short diagonal. Since the diagonals intersect at right angles, the triangle COD is rectangular. Half of the short diagonal OD is the leg of this triangle and can be found through the hypotenuse CD, as well as the OCD angle.
The diamonds of the rhombus are also the bisectors of its angles, so the OCD angle is α- / 2.
Thus, OD = BD / 2 = CD * sin (α- / 2). That is, the short diagonal BD = 2a * sin (α- / 2).
Similarly, from the fact that the triangle COD is rectangular, we can express the value of OC (and this is half the length of the long diagonal).
OC = AC / 2 = CD * cos (α- / 2)
The length of the long diagonal is expressed as follows: AC = 2a * cos (α- / 2)