How to determine the degree of angle
How to determine the degree of angle
The need to calculate the angles in degreeOh arises not only in the solution of various problemsfrom school textbooks. Despite the fact that most of us all this school trigonometry seems completely abstracted from life, sometimes it suddenly turns out that at hand there are no other ways to solve a purely practical problem other than school formulas. To measurement in degrees These angles are applicable to the full extent.
Instructions
1
If it is possible to use the appropriate measuring instrument, then select the one that best suits the task. For example, to determine the angledrawn on paper or other similarmaterial, the protractor is quite suitable, and to determine the angular directions on the terrain, it is necessary to search for a geodetic theodolite. To measure the angles between mating planes of any volumetric objects or aggregates, use goniometers-there are many types that differ in device, method of measurement, and accuracy. You can find more exotic angle measuring devices in degrees.
2
If the possibility of measuring withthere is no corresponding tool, then use the trigonometric relations known between schools between the lengths of the sides and the angles in the triangle. To do this, it will be enough to measure not angular, but linear dimensions - for example, using a ruler, roulette, meter, pedometer, etc. From this and start - measure from the top angle along two sides of it, a convenient distance, write down the values of these two sides of the triangle, and then measure the length of the third side (the distance between the endings of these sides).
3
Select to calculate the value angle at degrees one of the trigonometric functions. For example, we can use the cosine theorem: the square of the length of the side lying opposite to the measured angle, is equal to the sum of the squares of the other two sides, reduced by twice the product of the lengths of these sides by the cosine of the desired angle (a² = b² + c²-2 * b * c * cos (α)). From this theorem output the cosine value: cos (α) = (b² + c²-a²) / (2 * b * c). Trigonometric function, which from the cosine recovers the value angle at degrees, is called the arc cosine, which means that the formula in the final form should look like this: α = arccos ((b² + c²-a²) / (2 * b * c)).
4
Substitute the measured dimensions of the sides of the trianglein the formula obtained in the previous step and perform the calculations. This can be done using any calculator, including those that offer various online services on the Internet.
