In the field, it is sometimes very important and useful to possess the simplest applied methods of measuring on the ground. For example, ways to determine the height of a tree or any other object on the ground.

## Simple ways to determine the height of a tree or any other object by shadow, pole, puddle or mirror, right triangle.

The height of a tree or any other object on the ground can very easily be determined by a shadow, a pole, a puddle or a mirror, and a right triangle.

## The method of determining the height of a tree or other object by its height and length of the shadow.

If, on level ground, measure the length of your shadow, and then the length of the shadow cast by a tree or object, then the desired height can easily be calculated from the ratio:

**AK / ak = KE / ke**

where AK is the height of the tree (B), KE is the shadow of the tree (D), ak is your height (b), ke is your shadow (d).

For example, the length of your shadow d is three steps, the shadow of the tree D is nine steps, that is, the shadow of the tree is three times longer than your shadow. If you take your height for 1.5 meters, then the height of the tree will be B = 1.5 x 3 = 4.5 meters.

## The method of determining the height of a tree or other object by the pole and its height.

The same method can be applied in cloudy weather, when shadows from objects are not visible. In this case, to measure you need to take a six equal to the length of your height. This pole should be installed at a distance from the tree so that lying you can see the top of the tree in one straight line with the top point of the pole. Then the height of the tree is equal to the distance from your head to the base of the tree, i.e. AC = BC.

## The method of determining the height of a tree or other object by a puddle or mirror.

By a puddle, a mirror or a heliograph, the height of a tree or any other object on the ground can be measured as follows. Become so that the puddle fits between you and the tree (B). Find the point from which the top of the tree reflected in the water is visible. The measured tree will be so many times higher than you, how much the distance from it to the puddle (IN) is greater than the distance from the puddle to you (AO). Instead of a puddle, you can also use the mirror, laying it horizontally so as to see the top of the tree.

## The method of determining the height of a tree or other object using a rectangular triangle with two acute angles of 45 degrees.

Using a right-angled triangle with two acute angles of 45 degrees, the height of a tree or other object is determined as follows. Moving away from the tree a certain distance and applying a triangle to the eyes so that one of its legs is parallel to the axis of the tree, the second is parallel to the earth’s surface, and the hypotenuse is a line of sight.

Then achieve such a position that the line of sight passes through the top of the tree. In this case, the height of the tree D is equal to the distance from the observer to the tree and plus the growth of the observer.

*Based on the book “Map and Compass My Friends”.*

* Klimenko A.I..*