Why do you use pythagorean theorem?

Answer 1

The Pythagorean theorem is used to describe the relationship of the hypotenuse (the longest side) of a right triangle to its other two sides, where a right triangle is described as a three-sided shape where the angle between two of its sides is square, or 90 degrees.

We can use the theorem, for example, to determine the shortest linear distance between one point and another, as long as we know how far to it is away in two directions. To wit:

If I know that an apple is 4 feet to the right of me and 3 feet in front of me, the shortest distance to the apple is directly along the hypotenuse of the triangle formed by joining those two "legs" of the trip. Since the question does not venture into how the theorem is calculated, I will simply leave off with some related comments:

1) It is important to note that there are other theorems for solving triangles. Triangulation, perhaps best attributed in today's age to locating a cell phone making an emergency call, might use the Law of Sines to find the phone. Indeed, the Law of Cosines reduces to the pythagorean theorum when it is used on a right triangle.

2) It is shortsighted to assume that the theorem is only useful in 2-dimensional geometry. It is in fact extremely important in 3D, not only because our games' virtual environments are drawn in triangles (where many video cards rate how many triangles can be drawn per unit of time), but also because engineering depends on a basic understanding of how much force pushes in two directions, which leads to how much it pushes in a third direction. While this is a basic description because we're actually dealing with three dimensions, this theorem is fundamental to such calculations.

3) Related to engineering, it is also possible to determine the heights of things that would be difficult to measure otherwise. It's not practical to drill a hole through the peak of a mountain to its base in order to determine its height by dropping a tape measure down the hole. It is practical to take measurements from some point at the base to a locater at the the top (giving the hypotenuse), determine the horizontal distance from the centerline of the mountain to your position (giving another leg), and rearranging the theorem--using basic rules of algebra--to determine the vertical distance to the top.

4) More advanced math utilize properties of this formula to continue to more interesting problems, but that is outside of the scope of this question. The short answer is: our scientists, engineers, designers, and people of all professions use the theorem to answer some very basic questions about measurements made in their respective fields.