The rhombus is formed of a square at extension of a figure for the tops located on one diagonal. Two corners become less straight lines. Two other corners increase, turning into stupid.
Instruction
1. The sum of four internal corners of a rhombus is equal 360 °, as at any quadrangle. Opposite corners of a rhombus are equal, at the same time always in one couple of equal corners — acute angles, in another - stupid. Two corners adjacent to one party in the sum make the developed corner. Rhombuses with an identical size of the party can differ externally very strongly from each other. This distinction is explained by the different size of internal corners. Therefore, for finding of a corner of a rhombus the nobility only its party is not enough.
2. Knowledge of diagonals of a figure is sufficient for determination of size of corners of a rhombus. After carrying out in a rhombus of both diagonals the rhombus will be broken into four triangles. Diagonals of a rhombus are located at right angle, therefore, the received triangles are rectangular. A rhombus — a symmetric figure, its diagonals are at the same time symmetry axes therefore all internal triangles are equal. Acute angles of the triangles formed by rhombus diagonals are equal to a half of corners of a rhombus which need to be found.
3. The tangent of an acute angle of a rectangular triangle is equal to the relation of legs, opposite to adjacent. A half of each diagonal of a rhombus is a leg of a rectangular triangle. If big and small diagonals of a rhombus to designate d ₁ and d ₂ respectively, and rhombus corners — And (sharp) and In (stupid), then in rectangular triangles in a rhombus follows from a ratio of the parties: tg (A/2) (d /2) / (d /2) =d /d ₁, tg(B/2)= (d /2) / (d /2) =d /d ₂.
4. On a formula of a double corner tg (2α) = 2 / (ctg α - tg α) find tangents of corners of a rhombus: tg A = 2 / ((d /d ₂)-(d /d ₁)) and tg B =2 / ((d /d ₁)-(d /d ₂)). According to trigonometrical tables find the corners corresponding to the calculated values of their tangents.