Each trapeze has two sides and two bases. To learn the area, perimeter or other parameters of this figure, it is necessary to know at least one of sides. Also quite often under the terms of tasks it is required to find side of a rectangular trapeze.
Instruction
1. Draw a rectangular trapeze of ABCD. Designate sides of this figure, respectively, as AB and DC. The first side of DC coincides with trapeze height. It is perpendicular to two bases of a rectangular trapeze. There are several ways of finding of sides. So for example, if in a task the second side of BA and a corner ABH=60 is given, then find the first height the simplest of ways, having carried out BH height: BH=AB*sinαПоскольку BH=CD, СD=AB*sinα= √ 3AB/2
2. If, on the contrary, the party of a trapeze designated as CD is given, and it is required to find its party AB, such task decides in a bit different way. As BH=CD, and at the same time, BH represents ABH triangle leg, it is possible to draw a conclusion that the party of AB is equal: AB=BH/sinα=2BH / √ 3
3. The problem can be solved and in case values of corners are unknown provided that two grounds and side of AB are given. However, in this case it is possible to find only side of CD which is trapeze height. Originally, knowing values of the bases, find AH piece length. It is equal to the difference of the bigger and smaller bases as it is known that BH=CD:AH=AD - VSZatem, using Pythagorean theorem, find BH height equal to side of CD: BH= √ AB^2-AH^2
4. If the rectangular trapeze has a diagonal of BD and a corner 2α, as shown in figure 2, then the party of AB can be found also on Pythagorean theorem. For this purpose, at first calculate AD basis length: Find AD=BD*cos2αЗатем the party of AB as follows: √ BD^2-AD^2После of it prove to AB= similarity of triangles of ABD and BCD. As at these triangles one general party - diagonal, and at the same time, two corners are equal, apparently from the drawing, these figures are similar. On the basis of this proof find the second side. If the top basis and diagonal is known, then find the party usually with use of the standard theorem of cosines: c^2= а^2+b^2-2ab cos α, where and, b, with - the parties of a triangle, α - a corner between the parties and and b.