If we calculate the perimeter (P) of an octagon is necessary in theory, but in the original terms of the lengths of all sides of this figure (a, b, c, d, e, f, g, h), add these values: P = a+b+c+d+e+f+g+h. To know the lengths of all sides are necessary only in the case of an irregular polygon, and if the conditions of the problem know that the figure is correct, it will be quite the length of one hand - just increase it eight times: P = 8*a.
If the original data says nothing about the length of sides of a regular octagon, but given the radius described about the shape of the circle (R), before application of the formula from the previous step will have to calculate the missing variable. Each side of this octagon can be considered an isosceles triangle, the sides of which are radii of the circle. Since most of these similar triangles is eight, the angle between the radii of each of them will be one-eighth part of a complete turn: 360°/8 = 45°. Knowing the lengths of two sides of a triangle and the angle between them, determine the magnitude of base - the cosine of half the angle and multiply by twice the length of the side: 2*R*cos(22,5°) ≈ 2*R* 0,924 ≈ R* 1,848. Substitute the value obtained into the formula from the first step: P ≈ 8*R*1,848 ≈ R*14,782.
If the conditions of the problem given only the radius (r) inscribed in the regular octagon of the circle, it is necessary to perform calculations similar to those described above. In this case, the radius can be represented as one of the legs of a right triangle, the other leg of which is half of the desired side of the octagon. The acute angle adjacent to the radius will be two times less calculated in the previous step: 360°/16 = 22,5°. The length of the right side calculate by multiplying the tangent of that angle on the other side (radius), and to determine the amount of sides of the octagon resulting value double: 2*r*tg(22,5°) ≈ 2*r*0,414 ≈ r*0,828. Substitute this expression into the formula from the first step: P ≈ 8*r*0,828 ≈ r*6,627.
If you calculate the radius required by the method of practical dimensions, depending on the figure size, use, for example, line, odometer ("rolling meter") or a pedometer. The obtained values of the lengths of the sides put in one of the two formulas given in one of the steps.
Advice 2: How to calculate directional angle
Orientation in the field an important component of many professions. To do this, use maps and compasses. To determine the direction on the map for a specific object use directional angle and magnetic azimuth.
You will need
- Compass or compass, sharpened pencil, ruler, protractor.
Directional angle in surveying is called the angle between the line passing through the given point the direction of the reference point and the line parallel to the x-axis, otchityvanie from the North direction to the x-axis. It counts from left to right (in the direction of the arrow) from 0 ╟ to 360°.
It is most convenient to determine the direction on the map. Pencil, ruler, draw a line through the centers of the symbols, a starting point and guide. Length of a line drawn, for convenience of measurement, should exceed the radius of the protractor. After that, align the center of the protractor with the point of intersection of the lines and rotate it so that zero on protractor coincides with vertical grid line on the map (or a line parallel thereto). The value of the angle count in the direction of clockwise. The average measurement error directional angle protractor is 15/ 1o.
Sometimes, for calculating directional angles using magnetic azimuths. Magnetic azimuth is the horizontal angle formed by the line directed to the reference point and the North direction of the magnetic Meridian. He also counts from 0 ╟ to 360 ° clockwise. Magnetic azimuths are measured on the ground using a compass or bussoli. Needle of a compass, its magnetic field interacts with the magnetic field location and shows the direction of the magnetic Meridian.
Next, you need to determine the correction direction (the amount of convergence of the meridians and magnetic declination). Magnetic declination is called the angle between the magnetic and geographical meridians at a given point. The convergence angle is the angle between the tangent to the local Meridian and the tangent to the surface of the ellipsoid of rotation, carried out at the same point, parallel to the initial Meridian. The amendment directions are also measured from the North direction of a grid in the direction of clockwise. The amendment direction is considered positive, if the arrow is deflected to the right (East) and negative if it deviates to the left (to the West). Measured using bussoli on the ground magnetic azimuth can be translated in the direction adding an amendment to the draft directions carefully considering the sign of the amendment.
On many maps often indicate the value of the convergence of meridians (also called Gaussian approximation)and amendments directions
Pay special attention to the direction of reference and heed all signs.