Knowledge of all three parties in a rectangular triangle more than is enough for calculation of any of its corners. So it is a lot of this information that you even have an opportunity to choose which of the parties to involve in calculations to use most to you nice trigonometrical function.
Instruction
1. If you prefer to deal with an arcsine, use hypotenuse length in calculation (C) - the longest party - and that leg (A) which lies opposite to a required corner (α). Division of length of this leg into length of a hypotenuse will give the size of a sine of a required corner, and the return to a sine function - an arcsine - from the received value will restore corner size in degrees. Therefore use such formula in calculations: α = arcsin(A/C).
2. For replacement of an arcsine with an arccosine involve in calculations of length of those parties which form a required corner (α). One of them will be a hypotenuse (C), and another - a leg (C). By definition the cosine is the relation of length of a leg, adjacent to a corner, to hypotenuse length, and from value of a cosine the function an arccosine is engaged in restoration of a corner. Use such formula of calculations: α = arccos(B/C).
3. It is possible to use in calculations and an arctangent. For this purpose you need lengths of two short parties - legs. The tangent of an acute angle (α) in a rectangular triangle is defined by the relation of length of the leg (A) lying opposite to it to length of an adjacent leg (C). By analogy with the options described above use such formula: α = arctg(А/B).
4. The same parties - legs And yes In - are necessary also when using an arc cotangent in a formula of calculation of an acute angle (α) of a rectangular triangle. For obtaining value of a cotangent the dividend and a divider in definition of a tangent are enough to trade places therefore use such formula: α = arcctg (V/A).
5. If there is desire to use even more exotic trigonometrical functions, pay attention, for example, to inverse secant. You need the same couple of the parties, as in the second step - adjacent to a required corner (α) a leg (B) and a hypotenuse (C). But a dividend and a divider it is necessary to trade places therefore the formula in a final look will have such appearance: α = arcsec (S/V).
6. Couple to a secant is made by the function a cosecant determined by the hypotenuse length relation (C) to an opposite required corner (α) to a leg (A). To involve in calculations arkkosekans use such formula: α = arccsc (R/a).