The theorem of cosines in mathematics is most often used when it is necessary to find the third party on a corner and two parties. However, sometimes the statement of the problem is set on the contrary: it is required to find a corner at the set three parties.
Instruction
1. Imagine that the triangle at which lengths of two parties and value of one corner are known is given. All corners of this triangle are not equal each other, and its parties also are various in size. The corner γ lies opposite to the party of a triangle designated as AB which is the basis of this figure. Through this corner and also through the remained parties of AC and BC it is possible to find that party of a triangle which is unknown, according to the theorem of cosines, having removed the formula given below on its basis: a^2=b^2+c^2-2bc*cosγ where a=BC, b=AB, s=ASTeoremu cosines differently call the generalized Pythagorean theorem.
2. Now imagine that all three parties of a figure are given, but at the same time its corner γ is unknown. Knowing that formula has a type of a^2=b^2+c^2-2bc*cosγ, transform this expression so that the corner γ became required size: b^2+c^2=2bc*cosγ+a^2. Then lead the equation shown above to a bit different look: b^2+c^2-a^2=2bc*cosγ.Затем this expression should be transformed to given below: cosγ= √ b^2+c^2-a^2/2bc. It was necessary to substitute in a formula of number and to carry out calculations.
3. To find a cosine of the angle of the triangle designated as γ it it is necessary to express through the inverse trigonometrical function called an arccosine. An arccosine of number m is called such value of a corner γ for which the cosine of the angle γ is equal to m. The y=arccos m function is decreasing. Imagine, for example, that the cosine of the angle γ is equal to one second. Then the corner γ can be defined through an arccosine as follows: γ = arccos, m = arccos 1/2 = 60 °, where m = 1/2. The same way it is possible to find also other corners of a triangle at two other its unknown parties.
4. In case corners are presented in radians, transfer them to degrees, using the following ratio: π radian = 180 degrees. Remember that the vast majority of engineering calculators is supplied with a possibility of switching of units of measure of corners.