Rectangular call a triangle, the corner in one of tops of which is equal 90 °. The party lying opposite to this corner is called by a hypotenuse, and by the parties, opposite to two acute angles of a triangle, are called legs. If length of a hypotenuse and size of one of acute angles is known, then these data are enough to construct a triangle in, at least, two ways.
It is required to you
- Sheet of paper, pencil, ruler, compasses, calculator.
Instruction
1. The first way demands existence except a pencil and paper also a ruler, a protractor and the square. At first draw that party which is a hypotenuse - put A end, postpone from it the known length of a hypotenuse, put the end With and connect points.
2. Apply a protractor to the carried-out piece so that the zero mark coincided with A point, measure the size of the known acute angle and put the auxiliary end. Draw a line which will begin in a point of A and to pass through an auxiliary point.
3. Apply the square to AC piece so that the right angle began from a point of C. The square of the line drawn on the previous step designate a point of intersection by letter B and connect it to a point of C. On it creation of a rectangular triangle with the known length of the party of AC (hypotenuse) and an acute angle in top of A will be finished.
4. Other way except a pencil and paper will demand existence of a ruler, compasses and the calculator. Begin with calculation of lengths of legs - knowledge of size of one acute angle and length of a hypotenuse for this purpose quite enough.
5. Calculate length of that leg (AB) which lies opposite to a corner of the known size (β) - it will be equal to the work of length of a hypotenuse (AC) on a sine of the known corner of AB=AC*sin(β).
6. Determine length of other leg (BC) - it will be equal to the work of length of a hypotenuse on a cosine of the known corner of BC=AC*cos(β).
7. Put A end, measure from it hypotenuse length, put the end of C and draw between them a line.
8. Postpone length of a leg of AB calculated in the fifth step on compasses and draw an auxiliary semicircle with the center in A point.
9. Postpone length of a leg of BC calculated in the sixth step on compasses and draw an auxiliary semicircle with the center in the Page point.
10. Note a point of intersection of two semicircles letter B and carry out pieces between points of A and B, C and B. On it creation of a rectangular triangle will be complete.