The Pythagorean Theorem is used quite often in calculating distances between two points. This comes up in surveying for analyzing land when determining where to put roads and buildings. In addition, it will arise when calculating the distances to inaccessible objects. That is, you use the Pythagorean Theorem in conjunction with trigonometry when finding the width of a river if you cannot measure the width directly, or the height of a large building.
As a more whimsical example, the LCD dimensions for laptops are often given in terms of the length of the diagonal of the screen. However, the manufacturer would not need to measure the diagonal length, but instead use the Pythagorean Theorem to calculate it based on the height and width of the screen.
There are many practical application of Pythagoras theorem.Some of them are:
When you are dividing a land into rectangular pieces, you can check id the land is rectangular or not. For this measure the length, breadth and diagonal of the area. Then find the value of diagonal using pythagras theorem. If the answer and practical measurement is near then the area is fairly rectangular else it is not.
It can also be used to calculat the length of ropes required to fix a pole.
These are some everyday exaples. Besides this theorrem is exttensively used in astronomy to know the distance between the heavenly bodies and also to find terrestial distances