Trapeze — a certain type of a quadrangle. Two of four parties of this figure are parallel and are called big and small the bases. Two other parties are considered as side.
It is required to you
- - pencil
- - ruler
Instruction
1. Carry out a beam of any length from any point on the plane. Let's consider that the basis of a trapeze is located on this beam. From a starting point carry out the piece equal to the known party of a trapeze under the corner set in a task. If to solve a problem in a general view, then for implementation of the drawing it is possible to carry out by hand a piece of any size at an angle, smaller 90 degrees. However, the sizes of side and its inclination chosen randomly to the trapeze basis, are unambiguously certain and cannot change.
2. From the end of side carry out the beam parallel to the first. At you a part of a trapeze with the known side and unambiguously certain corners between this party and the bases of a trapeze turned out. It is obvious that the distance between the bases or height of a trapeze has strictly certain value: h=a*Sin αгде h-trapeze height, and — side, α — the known corner.
3. Whether perhaps according to a task to learn something else about the considered trapeze and to find its basis? Between side and one of the bases it is possible to determine a corner between this party and the second basis as the sum of these corners is always equal in a trapeze to 180 degrees by the set corner, but it is impossible to learn something about the size of the bases.
4. Very useful would be an information on the diagonal of a trapeze or its average line. Average to the line of a trapeze not only is parallel to the bases, but also is in number equal to their half-sum, and this property gives the chance to receive the answer to a question of basis size. In the presence of the known diagonal the task can be reduced to finding of the third party of a triangle on two known. But on knowledge only of a corner and side of a trapeze unambiguously it is impossible to solve a problem of finding of its basis.