Two short parties of a rectangular triangle which it is accepted to call legs by definition have to be perpendicular among themselves. This property of a figure considerably facilitates its construction. However an opportunity to precisely define perpendicularity is not always. In such cases it is possible to calculate lengths of all parties - they will allow to construct a triangle unique and therefore correct, way.

## It is required to you

- Paper, pencil, ruler, protractor, compasses, square.

## Instruction

1. If it is required to draw a rectangular triangle of any sizes, then begin with one of legs. Put the end which will be top 90 ° a corner, and carry out horizontal a piece of suitable length. Then from the same point carry out a vertical piece - the second leg. It has to be strictly perpendicular to the horizontal party of a triangle.

2. If the paper used for construction is not marked "in a section", then use the square for such construction. If it is absent, involve a protractor. Then connect both pieces the third line - it will be a hypotenuse of a rectangular triangle. On it construction will be complete.

3. If it is required to construct a figure with the parameters set in initial conditions, then carrying out preliminary calculations can be required. In the absence of paper in a section, a protractor and the square for construction it is necessary to know lengths of all parties of a triangle. If not all of them are given in initial conditions, then it is necessary to calculate missing by the known formulas.

4. With the known lengths of two legs determine length of the third party according to Pythagorean theorem - square each of lengths, put results and take a square root from the received value. And if in conditions length of a hypotenuse and size of one of acute angles is given, then at first use the theorem of sine of a plant louse of finding of length of one of legs - increase length of the known party by a sine of this corner. Then determine length of other leg by Pythagorean theorem. Similarly calculate lengths at other sets of basic data.

5. Begin construction when lengths of all parties are calculated. Put the end to top of future right angle and on a ruler carry out a piece with a length of one from legs. Then postpone length of a hypotenuse on compasses and carry out a semicircle with the center at the end of this piece - it has to be directed towards the end put to the beginning of construction.

6. Postpone length of the second leg on compasses, establish it in the same initial point and note the place of crossing of a nacherchenny semicircle with the imagined circle of the measured radius. Then connect noted place to the initial point (it will be the second leg) and to the termination of the piece which is carried out earlier (it is a hypotenuse). On it construction will be complete.