The triangle, one of corners of which is to straight lines (it is equal 90 °), call rectangular. Its longest party always lies opposite to a right angle and is called a hypotenuse, and two other parties are called legs. If lengths of these three parties are known, then it is possible to find sizes of all corners of a triangle as actually it will be required to calculate only one of corners. It is possible to make it in several ways.
Instruction
1. Use for calculation of sizes of corners (α, β, γ) definitions of trigonometrical functions through a rectangular triangle. Such definition, for example, for a sine of an acute angle is formulated as the relation of length of an opposite leg to hypotenuse length. Means if lengths of legs (A and B) and hypotenuses (C) are known, to find, for example, a sine of the angle α, the leg of A lying opposite it is possible, having divided length of the party And into length of party of C (hypotenuse): sin(α) = A/C. Having learned value of a sine of this corner it is possible to find its size in degrees, having used the return to a sine function - an arcsine. That is α=arcsin (sin(α))=arcsin(A/C). It is possible to find the same way also the size of other acute angle in a triangle, but in it there is no need. As the sum of all corners of a triangle always is 180 °, and one of corners is equal in a rectangular triangle 90 °, the size of the third corner can be counted as the difference between 90 ° and the size of the found corner: β=180 ° -90 °-α=90 °-α.
2. Instead of definition of a sine it is possible to use definition of a cosine of an acute angle which is formulated as the relation of length of a leg, adjacent to a required corner, to hypotenuse length: cos(α) = B/C. And here use inverse trigonometrical function (arccosine) to find corner size in degrees: α=arccos (cos(α))=arccos(B/C). After that, as well as in the previous step, it will be necessary to find the size of a missing corner: β=90 °-α.
3. It is possible to use similar definition of a tangent - it is expressed by a ratio of length opposite to a required corner of a leg to length of a leg adjacent: tg(α) = A/B. Again determine corner size in degrees through the inverse trigonometrical function - an arctangent: α=arctg (tg(α))=arctg(A/B). The formula of size of a missing corner will remain without changes: β=90 °-α.