The word "leg" comes from the Greek words "perpendicular" or "steep" - it explains why quite so called both parties of a rectangular triangle making its ninety-degree corner. To find length of any of legs easily if the size of the corner adjoining to it and still any of parameters as in this case sizes of all three corners will become actually known is known.
Instruction
1. If except the size of an adjacent corner (β) length of the second leg (b) is known, then length of a leg (a) can be determined as private from division of length of the known leg into a tangent of the known corner: a=b/tg(β). It follows from definition of this trigonometrical function. It is possible to do without tangent if to use the theorem of sine. Follows from it that the relation of length of the required party to a sine of an opposite corner is equal to the relation of length of the known leg to a sine of the known corner. Opposite the required leg can express an acute angle through the known corner as 180 ° -90 °-β = 90 °-β as the sum of all corners of any triangle has to be 180 °, and by definition of a rectangular triangle one of its corners is equal 90 °. Means, the required length of a leg can be calculated on a formula a=sin (90 °-β) ∗ b/sin(β).
2. If are known the size of an adjacent corner (β) and length of a hypotenuse (c), then length of a leg (a) can be calculated as the work of length of a hypotenuse on a cosine of the known corner: a=c∗cos(β). It follows from definition of a cosine as trigonometrical function. But it is possible to use, as well as in the previous step, the theorem of sine and then length of a required leg will equal to the work of a sine of a difference between 90 ° and the known corner on the hypotenuse length relation to a sine of a right angle. And as the sine 90 ° is equal to unit, the formula can be written down so: a=sin (90 °-β) ∗ with.
3. Practical calculations can be made, for example, by means of the program calculator which is available as a part of Windows OS. For its start it is possible in the main menu on the Start-up button to select the Implement clause, to make the calc team and to press the OK button. Trigonometrical functions are not provided in the simplest version of the interface of this program opening by default therefore after its start it is necessary to click in the menu the section "Look" and to choose the line "Scientific" or "Engineering" (depends on the used version of the operating system).