Need for calculation of sizes of corners for degrees arises not only at the solution of various tasks from school textbooks. In spite of the fact that all this school trigonometry seems to most of us absolutely idealistic abstraction, sometimes suddenly it becomes clear that near at hand there are no other ways of the solution of purely practical task except school formulas. In degrees of sizes of corners it is fully applicable to measurement.
Instruction
1. If there is an opportunity to use the corresponding measuring device, then choose that which in the greatest measure corresponds to an objective. For example, for determination of size of a corner nacherchenny on paper or other similar material, the protractor quite will approach, and for definition of the angular directions on the area it is necessary to look for a geodetic theodolite. For measurements of sizes of corners between the interfaced planes of any volume objects or units use angle meters - them exists many types differing in the device, method of measurements and accuracy. It is possible to find also more exotic devices of measurement of corners in degrees.
2. If the possibility of measurements by means of the corresponding tool is absent, then use the trigonometrical ratios, known from school, between lengths of the parties and sizes of corners in a triangle. For this purpose there will be enough opportunity to measure not the angular, but linear sizes - for example, by means of a ruler, a roulette, meter, a pedometer, etc. Also begin with it - measure from vertex of angle along two of its parties distance convenient to you, write down sizes of these two parties of a triangle, and then measure also length of the third party (distance between the terminations of these parties).
3. Choose for calculation of size of a corner in degrees one of trigonometrical functions. For example, it is possible to use the theorem of cosines: the square of length of the party lying opposite to the measured corner is equal to the sum of squares of two other parties reduced by the doubled work of lengths of these parties on a cosine of a required corner (a² = b²+c²-2*b*c*cos(α)). Bring value of a cosine out of this theorem: cos(α) = (b²+c²-a²) / (2*b*c). Trigonometrical function which of a cosine restores corner size in degrees is called an arccosine, and it means that the formula in a final look has to look so: α = arccos ((b²+c²-a²) / (2*b*c)).
4. Substitute the measured sizes of the parties of a triangle in the formula received on the previous step and make calculations. It can be done by means of any calculator, including also what is offered by various online services on the Internet.