Rhombus call a quadrangle at which all parties are identical, and corners are not equal. This geometrical figure has unique properties which considerably facilitate calculations. To find its bigger corner, it is necessary to know some more parameters.
It is required to you
- - table of sine;
- - table of cosines;
- - table of tangents.
Instruction
1. In statements of the problem the smaller corner can be specified. Remember what the sum of the corners adjacent to one party is equal to. It at any rhombus makes 180 °. That is you have enough from 180 ° to subtract size of the known corner. Draw a rhombus. Designate a bigger corner as α, and smaller – as β. The formula will look in this case as α=180 °-β.
2. In a task also the size of the party and length of one of diagonals can be specified. In this case it is necessary to remember properties of diagonals of a rhombus. In a point of intersection they are halved. Diagonals are perpendicular each other, that is at the solution of a task it will be possible to use properties of rectangular triangles. One more important detail each of diagonals at the same time is also a bisector.
3. For descriptive reasons make the drawing. Draw ABCD rhombus. Carry out in it diagonals of d1 and d2. Let's say the diagonal of d1 known to you connects smaller corners. Designate a point of their crossing as Oh, big corners of ABC and CDA-as α, and smaller – as β. Each of corners is halved by diagonal. Consider a rectangular triangle of AOV. The parties of AB and OA, d1 equal to a half of diagonal are known to you. They represent a hypotenuse and a leg of an opposite corner.
4. Calculate AVO sine of the angle. It is equal to OA leg relation to AV hypotenuse, that is sinABO = to OA/AB. According to the table of sine find the corner size. Remember that it is equal to a half of a bigger corner of a rhombus. Respectively, for definition required increase the received size by 2.
5. If in conditions the size of diagonal d2 connecting big corners is given, the way of the decision will be similar previous, only instead of a sine the cosine – the relation of an adjacent leg to a hypotenuse is used.
6. In conditions only the sizes of diagonals can be set. In this case the drawing, but, unlike the previous tasks is required too, it can be exact. Carry out d1 diagonal. Halve it. To a point of intersection carry out d2 diagonal so that it was divided into two equal parts too. Connect the ends of pieces on perimeter. Designate a rhombus as ABCD, a point of intersection of diagonals – as the Lake.
7. In this case you do not need to calculate the party of a rhombus. You formed a rectangular triangle of AOV at which two legs are known to you. The relation of an opposite leg to adjacent is called a tangent. To find tgABO, divide OA into OV. Find the necessary value of a corner in the table of tangents, and then increase it by two.
8. Some computer programs allow not only to calculate a bigger corner of a rhombus in the set parameters, but also at once to draw this geometrical figure. It can be done, for example, in the AutoCAD program. In this case tables of sine and tangents, of course, are not necessary.