It is possible to define distance between two points, having measured length of a piece which is under construction between them. If coordinates of points are known, then the distance can be calculated, using mathematical formulas.

## It is required to you

- - ruler;
- - range finder;
- - angle meter;
- - concept about the Cartesian coordinates.

## Instruction

1. To measure distance between two points, construct a piece which ends will be these points. Then, by means of a ruler measure length of this piece. It will also be equal to distance between two points. It can be done both in space, and on the plane.

2. If points have coordinates in the Cartesian system of coordinates (x1; y1; z1) and (x2; y2; z2) that to find distance between them make the following actions: 1. From coordinates of the first point, take away the corresponding coordinates of the second point, receive values (x1-x2); (y1-y2); (z1-z2). 2. Build the values received in item 1 in a square and find their sum (x1-x2)²+(y1-y2)²+(z1-z2)². 3. From the turned-out number take a root square.

3. The distance between points with coordinates will be result (x1; y1; z1) and (x2; y2; z2). If points are set in polar coordinates, transfer them to Cartesian. Find distance between them by the described technique.

4. If to install the system of coordinates it is problematic, and it is difficult to measure distances between two points on a straight line (for example if between points there is a hillock), use additional construction. Recede on the flat area until both of these points become visible. By means of a range finder measure distance to each of points (for best accuracy use laser measuring devices). Determine a corner between the directions on points between which distance is defined by the angle meter.

5. Find required distance, having done the following calculations: 1. Square the distances measured by a range finder and find the sum of the turned-out numbers. 2. Find the doubled work of the same distances and increase it by a cosine of the measured corner.3. From the result received in item 1 take away the result received in item 2. 4. Take a root from the received number square.