The protractor "by one's own hands"

In some cases, for example, during a country walk, you have to roughly measure the angles. But even the simplest homemade goniometer is not always under the arm. In such cases, our own fingers will help - the protractor "with our own hands", which is always with us. Of course, the measurements will be rough approximations, but still, more reliable than the estimation just by eye. But, in order to learn how to use such a goniometer, you must first make several measurements and calculations.

First of all, we need to establish from what angle we see the fingernail of the index finger of its outstretched arm. The usual width of the nail is 1 centimeter, and its distance from the eye in this position is about 57 cm; so we see it, approximately, at an angle of 1⁰.

Knowing this, it's easy to use a protractor made by "yourself" to evaluate small angles of view. Each distant object, which is just covered with the fingernail of the index finger of the elongated arm, is seen at an angle of 1⁰, and, therefore, is moved 57 times further than its diameter. If the nail covers half the object, then its angular value is 2⁰, and the distance is equal to 28 widths. The full moon covers only half of the nail, that is, it is visible at an angle of 1/2⁰, which means that we are 114 inches across.

The protractor, made by "own hands" will help and for corners more. Only for this purpose it is necessary to use the nail joint of the thumb, keeping it bent on the outstretched arm. In an adult, the length of this joint is about 3,5 cm, and the distance from the eye, with an elongated arm - about 55 cm. Its angular value in this position is 4⁰. This gives a means to estimate the viewing angles in 4⁰, and therefore 8⁰. With your own hands, you can measure two more angles: between the middle and index fingers, placed as widely as possible - 7-8⁰ and between the large and the index, also dilated to the greatest extent - 15-16⁰, with an outstretched arm.

Cases apply a protractor made by "own hands" while walking through open countryside there may be many. Let in the distance you see a freight car, which is covered, approximately, half the joint of the thumb of the outstretched arm, that is, it is visible at an angle of about 2⁰. Since the length of the freight car is about 6 meters, it is easy to find what approximate distance to it: 6*28 = 168 meters.

Using such a protractor made "by one's own hands" you can, for example, measure the angular height of the stars above the horizon, the mutual removal of stars in degrees, the apparent dimensions of the meteor's fiery path. Being in the position of Robinson and using the self-made protractor to measure angles and legs for measuring distances, it is easy to calculate for a variety of needs.