Arc is part of a circle contained between two points lying on this circle. Any arc can be expressed via numeric values. Its main characteristic along with the long is the value of the degree measure.
Degree measure of arc as the angle, measured in the degrees, of which 360, or in minutes, which in turn are divided into 60 seconds. The letter arc is indicated by the icon, which resembles the lower part of the circle and letters: two capital (AV) or one small letter (a).
But the allocation on the circumference of one arc involuntarily formed the other. Therefore, in order to clearly understand what an arc it is, tick on the selected arc another point, for example, C, Then the designation will change to ABC.
Segment formed by two points, the bounding arc is a chord.
Degree measure of arcs can be found using the value of an inscribed angle that, having vertex point on the circle based on the arc. Such an angle is inscribed in mathematics and its degree measure is equal to half the arc on which he relies.
Also in the circle there is a Central angle. It also depends on the desired arc, and its top is not on the circumference, and in the center. And its numeric value is already not part of the degree measures of the arc and its integer value.
Understand how to calculate arc based on her angle, you can apply this law in reverse and deduce the rule that the inscribed angle, which relies on the diameter, is direct. Because the diameter divides the circumference into two equal parts, then any of the arcs has a value of 180 degrees. Therefore, the inscribed angle is 90 degrees.
Also, based on the method of finding the degree value of the arc is just a rule for the angles based on the same arc, are equal.
The value of the degree measure of an arc is often used to calculate the circumference of a circle or arc. To do this, use the formula L= π*R*α/180.
Advice 2: How to find the degree measure of angle
Measure flat of angles in degrees was invented in ancient Babylon long before our era. The people of the state preferred a sexagesimal system of calculation, so division corners on 180 or 360 units today looks a little weird. However, proposed in the modern system of SI units, multiples of the number PI, not less weird. These two options are not limited to the currently used designations of angles, so the task of translating their values in degree measure arises quite often.
If the degree measure of the need to translate the measure of the angle in radians, assume that one degree corresponds to the number of radians equal to 1/180 fraction of PI. This mathematical constant has an infinite number of decimal places, so the conversion factor from radians to degrees is also an infinite decimal fraction. This means that an absolutely exact value in decimal fractions to not work, so the conversion factor should be rounded to. For example, with a precision of a billionth fraction of a unit calculated ratio is equal to 0,017453293. After rounding to the desired number of characters, divide by this factor the initial number of radians and you will get a degree angle.
In solving mathematical tasks from the topics that are related to geometry, often there are formulas in which values of angles are radians and fractions of PI. If you get a solution that contains this constant, to convert it to degrees, replace π by the number 180. For example, if the Central angle is defined by the expression π/4, this means that its degree measure is equal to 180°/4=45°.
Angles can be expressed in units, which are called "revolution." This unit corresponds to 360°, so the problems with conversion should not occur. For example, if the task says about the angle in a turn and a half, this corresponds to 360 x 1.5=540° in degree measure.
Sometimes in geometry problems is referred to an obtuse angle. It is formed by two rays, called opposite direction, that is, collinear. Use the number 180 for the expression values of the expanded angle in degrees.
In geodesy, cartography, astronomy degrees are divided into still smaller units, which have their own names, minutes and seconds. This division has roots in the same place and degrees, so each degree comprises 60 minutes, or 3600 seconds. Use these numbers if seconds and minutes need to be replaced in tenths of a degree. For example, angle 11°14'22" corresponds to a decimal fraction, approximately equal to 11 + 14/60 + 22/3600 if 11,2394°.