The special case of a parallelogram - a rectangle – is known only in Euclid's geometry. At a rectangle all corners are equal, and each of them separately makes 90 degrees. Proceeding from private properties of a rectangle and also from properties of a parallelogram about parallelism of the opposite parties it is possible to find the parties of a figure on the set diagonals and a corner from their crossing. Calculation of the parties of a rectangle is based on additional creation and use of properties of the received figures.
Instruction
1. Construct EFGH rectangle. Write down the known data: diagonal of a rectangle of EG and a corner α, received from crossing of two equal diagonals of FH and EG. Construct in the drawing of diagonal and note between them a corner α.
2. Letter A note a point of intersection of diagonals. Consider EFA triangle formed by constructions. According to property of a rectangle of its diagonal are equal and are halved by a point of intersection of A. Vychislite of FA and EA value. As the triangle of EFA is isosceles and its parties of EA and FA are equal among themselves and are respectively equal to a half of diagonal of EG.
3. Further calculate the first party of EF of a rectangle. This party is the third unknown party of the considered EFA triangle. According to the theorem of cosines on the corresponding formula find the party of EF. For this purpose substitute the values of the parties of FA received earlier in a formula of cosines EA and a cosine of the known corner between them α is equal. Calculate and write down the received EF value.
4. Find the second party of a rectangle of FG. For this purpose consider other triangle of EFG. It is rectangular where the hypotenuse of EG and a leg of EF are known. According to Pythagorean theorem find the second leg of FG on the corresponding formula.
5. According to properties of a rectangle his opposite edges are equal. Thus the party of GH is equal to the found party of EF, and HE = to FG. Write down all calculated parties of a rectangle in the answer.