Two parties of a triangle forming its right angle are perpendicular the friend the friend, as found reflection in their Greek name ("legs") today used everywhere. Each of these parties is adjoined by about two corners one of which to calculate there is no need (right angle), and another always is sharp and it is possible to calculate its size in several ways.
Instruction
1. If the size of one of two acute angles (β) of a rectangular triangle is known, then (α) more nothing is necessary for finding of another. Use the theorem of the sum of corners of a triangle in Euclidean geometry - as it (sum) is always equal 180 °, calculate the size of a missing corner subtraction of size of the known acute angle from 90 °: α=90 °-β.
2. If except the size of one of acute angles (β) lengths of both legs are known (And yes C), it is possible to use also other method of calculation - by means of trigonometrical functions. According to the theorem of sine of the relation of lengths of each of legs to a sine of an opposite corner are identical therefore (α) you find a sine of the necessary corner division of length of a leg, adjacent to it, into length of the second leg with the subsequent multiplication of result by a sine of the known acute angle. The trigonometrical function transforming value of a sine to the size corresponding to this value in angular degrees is called an arcsine - apply it to the received expression and you receive a final formula: α=arcsin (sin(β) * A/V).
3. If only lengths of both legs are known (And yes C), their ratios will allow to receive a tangent or a cotangent (depending on what to put in numerator) the calculated corner (α). Apply the inverse functions corresponding to them to these ratios: α = arctg (A/V) = arcctg (V/A).
4. If are known only length (C) a hypotenuse (length of the party) and the leg (B) adjacent to the calculated corner (α), then the relation of these lengths will give value of a cosine of a required corner. As well as for other trigonometrical functions, there is inverse function to a cosine (arccosine) which will help to bring out of this ratio corner size in degrees: α=arcsin (PREMIUM).
5. At the same basic data, as in the previous step, it is possible to use exotic trigonometrical function at all - a secant. It turns out division of length of a hypotenuse (C) at length of a leg (B), adjacent to the necessary corner, - you find inverse secant from this ratio of a plant louse of calculation of size of a corner, adjacent to a leg: α=arcsес (With/in).