The word "leg" came to Russian from Greek. In close translation it means a plumb, that is a perpendicular to the Earth's surface. In mathematics legs are called the parties forming a right angle of a rectangular triangle. Opposite to this corner the party is called a hypotenuse. The term "leg" is applied also in architecture and technology of welding works.
Draw a rectangular triangle of DIA. Designate its legs as and and b, and a hypotenuse — as page. All parties and corners of a rectangular triangle are connected among themselves by certain relations. The relation of a leg, opposite to one of acute angles, to a hypotenuse is called a sine of this corner. In this triangle of sinCAB=a/c. The cosine is the relation to a hypotenuse of an adjacent leg, that is cosCAB=b/c. The return relations are called a secant and a cosecant. The secant of this corner turns out at division of a hypotenuse into an adjacent leg, that is secCAB=c/b. Size, the return to a cosine turns out, that is it is possible to express it on a formula secCAB=1/cosSAB.
The cosecant is equal private from division of a hypotenuse into an opposite leg and it is size, the return to a sine. It can be calculated by a formula cosecCAB=1/sinCAB
Both legs are connected among themselves by a tangent and a cotangent. In this case the relation of the party of a to the party of b, that is an opposite leg to adjacent will be a tangent. This relation can be expressed by a formula tgCAB=a/b. Respectively, the cotangent will be the return relation: ctgCAB=b/a. The ratio between the sizes of a hypotenuse and both legs was defined still by the Ancient Greek mathematician Pythagoras. The theorem called by his name, people use still. It says that the square of a hypotenuse is equal to the sum of squares of legs, that is c2=a2+b2. Respectively, each leg will equal to a square root from the difference of squares of a hypotenuse and other leg. This formula can be written down as b= √ (s2-a2). Length of a leg can be expressed also through ratios known to you. According to theorems of sine and cosines, the leg is equal to the work of a hypotenuse on one of these functions. It is possible to express it and through a tangent or a cotangent. The leg and can be found, for example, on formula a = b*tan CAB. In precisely the same way, depending on the set tangent or a cotangent, also the second leg is defined. In architecture the term "leg" is also used. It is applied in relation to the Ionic capital and designates a plumb through the middle of its back. That is and in this case this term designates a perpendicular to the set line. In technology of welding works there is a concept "leg of an angular seam". As well as in other cases, this shortest distance. Here it is about an interval between one of the welded details to border of the seam which is on a surface of other detail.