Instruction
1
The sum of the four interior angles of a rhombus is equal to 360°, as in any quadrilateral. Opposite angles of a rhombus are equal, it is always one pair of equal angles — angles sharp, the other blunt. Two angles adjacent to the same side sum to a straight angle. Diamonds with the same size hand, may appear very different from each other. This difference is due to different values of internal angles. Therefore, to find the angle of a rhombus is not enough to know only his side.
2
Sufficient to determine the angles of a rhombus is the knowledge of the diagonals of the figure. After conducting the rhombus , both diagonals rhombus is divided into four triangles. The diagonals of a rhombus are located at a right angle, consequently, the resulting triangles are rectangular. Rhombus — symmetrical shape, its diagonals are both axes of symmetry, so all the internal triangles are equal. The sharp corners of the triangles formed by the diagonals of a rhombus is equal to half the angles of the rhombus that you need to find.
3
The tangent of an acute angle of a right triangle is the ratio of the sides opposite to the surrounding. Half of each diagonal of a rhombus is the leg of a right triangle. If the large and small diagonals of a rhombus to identify d₁ and d₂, respectively, and the angles of a rhombus — A (sharp) and (blunt), then the ratio of sides in right triangles inside the rhombus follows: tg (A/2)=(d₂/2)/(d₁/2)=d₂/d₁, tg(B/2)=(d₁/2)/(d₂/2)=d₁/d₂.
4
According to the formula of double angle tg (2α) = 2/(сtg α tg α) find the tangents of the angles of a rhombus: tg A = 2/((d₁/d₂)-(d₂/d₁)) and tan B =2/((d₂/d₁) to(d₁/d₂)). On trigonometric tables, find the angles corresponding to the calculated values of their tangents.