how do we use indirect measurements in the real world
There is a good definition and some examples of indirect measurements here:
http://www.icoachmath.com/Controls/IndirectMeasurement.html
An example would be determing a distance between two places on map, using the map scale to compute the actual distance.
Indirect measurements are often used when it is impractical, difficult, or impossible to make direct measurements. Here are a few examples of how indirect measurements are used in the real world:
1. Measuring the height of a tall building: It is often difficult to directly measure the height of a tall building. One indirect method is to measure the length of its shadow at a known time of day and determine the angle of elevation between the top of the building and the ground. From this information, you can use trigonometry to calculate the height of the building.
2. Determining the distance to a far-off object: When you want to measure the distance to a distant object, such as a mountain or a star, direct measurement is not feasible. Instead, you can use methods like triangulation (measuring angles from two or more known locations) or parallax (observing the apparent shift in position of the object from different viewpoints) to calculate the distance indirectly.
3. Estimating the population size: It may not be practical to directly count the entire population of a particular species in a large area. In such cases, researchers use statistical techniques, such as capturing and tagging a sample of individuals, then using that data to estimate the total population size.
4. Measuring the speed of a moving object: Directly measuring the instantaneous speed of a fast-moving object can be challenging. Doppler radar, however, provides an indirect measurement of an object's speed by analyzing the frequency shift of the waves that bounce off it.
In all these examples, indirect measurements involve using known principles, mathematical relationships, or specialized instruments to infer values that are otherwise difficult to directly observe or measure.