You will need
- - a sheet of paper;
- a pair of compasses;
- - the range;
- - protractor;
- - a computer with AutoCAD;
Construct a circle with a given radius. The principles of its construction in AutoCAD the same as on the sheet of paper. Having mastered the methods of constructing various geometric figures in the classical way, you will quickly understand how this is done on the computer. The difference is that in the ordinary construction with a compass you find the center of the circle at the point where you put the needle. In AutoCAD, look in the top menu click "arc" or "Arc". Choose build in the center, start point and angle and enter the desired parameters. Mark the center of the circle as O.
Using pencil and ruler or a computer mouse, swipe radius. If you draw on the sheet, then with a protractor lay aside a predetermined size of the angle. For this zero mark of the protractor will align with the dot On, check the desired angle and swipe through the resulting point of the second radius. Label the angle as α. You can call it as AOW, if appropriate letters to mark the points of intersection of the radii of the circle. You need to find the length of the arc AB.
If the size of the angle is specified in degrees, then arc length is equal to twice the product of the radius of the circle by a factor of π and the ratio of angle α to the full size of the Central angle of a circle. He is 360°. That is, it can be found by the formula L=2πRα/360°, where L is the desired arc length, R is the radius of the circle, and α is the size of an angle in degrees. The angle can be specified in radians. Then the arc length is equal to the product of the radius by the angle, i.e. L=RA. In this case, the rest of the formula has decreased in translating degrees to radian.
Designers often have to calculate the arc length, the value just estimated the height of the bridge or overlap and the span length. In this case, make a drawing. The span will be the chord and the height of the part radius. Swipe it from the top of the future arch is perpendicular to the chord and continue on to the intended center of the circle. The height divides the chord in half. The center will connect with the ends of the chord, thus obtaining a 2 radius. Calculate the radius by using the Pythagorean theorem, that is, R=√a2+(R-h)2.
Knowing the radius and the difference between him and the tall, by theorem of sines, find the magnitude of the half angle of the sector. Sine is the ratio of the opposite leg to the hypotenuse, i.e. sinα=a/R. In the table of sines to find the size of the angle and substitute it into the formula.
The two points divide the circle into two arcs. The job can be specified, the length of which one need to find. In this case, you must calculate the greater angle, and subtracting from the full angle given is acute.