Final answer:
The Pythagorean theorem, expressed as a² + b² = c², is used to calculate the straight-line distance between two points by relating the lengths of the sides of a right-angled triangle. It is practical for real-world distance measurements and can be paired with estimating techniques using familiar objects for scale.
Step-by-step explanation:
The Pythagorean theorem is a fundamental principle in geometry that relates the lengths of the sides of a right-angled triangle. This theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. This can be expressed as a² + b² = c², where a and b are the lengths of the legs and c is the length of the hypotenuse.
In practical terms, if you know the lengths of any two sides of a right-angled triangle, you can calculate the length of the third side using the Pythagorean theorem. This is especially useful in finding the straight-line distance between two points in real-world situations, such as the distance to a streetlight post when the other two distances are known. Moreover, when estimating distances in the absence of precise measurements, one can use known objects like the heights of trees, lengths of cars, or the widths of buildings as reference units to gauge the distance to a landmark.