Kristjan Salev

# LASER DISTANCE METER AND PYTHAGOREAN THEOREM

Updated: May 21

A laser distance meter (**LDM**) is a device used to determine the distance to an object with a laser beam. This device sends a pulse of laser light to the target and measures the time it takes until its turnback and converts this to a distance. It allows You to measure length, width, and height. Additionally, You can calculate surface areas and volumes. Compared with an old-fashioned measuring tape, this useful gadget has many advantages. It is more accurate, especially when measuring long distances and the line is always straight. You don't need anyone to help You with the measurement, and the measurement results are displayed in a fraction of a second. No need to worry about obstacles on the ground, as long there is a line of sight to Your target, and the target is within range. Vertical measurements can be made without the use of a ladder, thereby bringing more safety benefits.

One of the main disadvantages of using this device is its dependence on weather conditions. When measuring outdoors on a sunny day, laser points can be quite difficult to see. Similarly, if the target is very far away, the reflection may be a boor and this may affect the measurement result.

As mentioned, this device sends a pulse of laser light to the target and calculates the time it takes for the reflection to return. This is known as the " time of flight " principle. The distance equals speed times time. If the distance to the object is **D**, then the laser beam travels a total distance of **2D. **So the distance from the measuring device to the object can be found from the formula: **D = ct/2, **where **c **is the speed of light, and **t **equals the time for the round trip between **LDM** and the target.

Because the speed of light is **300 000 km/s (186 000 mi/s)**, measured time intervals are tiny. It takes a laser pulse of only **0,000000133** seconds** (133 nanoseconds) **to measure the distance to an object **20** meters **(65 ft) **away.

**Area** and **volume modes** are very easy to use. You only need to measure the length and width to get the area. In order to obtain the volume, the height must also be measured. The measuring device performs calculations according to the selected mode.

Using **Pythagorean mode 1**, You can measure the heights and lengths of different objects. let's say, for example, that you need to measure the height of a tree that cannot be measured in direct measurement mode. By measuring two lengths **a** and **b, ** LDM can calculate the missing third length (**x**) of a right triangle, using the Pythagorean theorem.

In **Pythagorean mode 2**, three measurements are made to obtain an unknown height or length. This becomes necessary when measurements are taken from a higher point. By measuring hypotenuses **a **and **b** and then the common right angle side **c** of the two triangles, The laser distance meter can find the unknown height** h** using the Pythagorean theorem.

In** Pythagorean mode 3**,** **You must also take three measurements **a, b**, and **c** to find the unknown height **h.**

Of course, You don't need to do the math yourself. The laser distance meter performs the calculations instantly once You have measured the required lengths.