## How is the Pythagorean Theorem used in the medical field?

2,500-year-old Pythagoras theorem helps to show when a patient has turned a corner. A medical researcher at the University of Warwick has found the 2,500 year-old Pythagoras theorem could be the most effective way to identify the point at which a patient’s health begins to improve.

**What does the Pythagorean Theorem say about the areas of squares?**

The sum of the areas of the two squares on the legs (a and b) equals the area of the square on the hypotenuse (c).

**What careers use the Pythagorean Theorem?**

Engineers and astronomers use the Pythagorean Theorem to calculate the paths of spacecraft, including rockets and satellites. Architects use the Pythagorean Theorem to calculate the heights of buildings and the lengths of walls.

### How does the Pythagorean Theorem relate to area?

Shape-Generalization Form of the Pythagorean Theorem: Given a right triangle, we can draw similar shapes on each side so that the area of the shape constructed on the hypotenuse is the sum of the areas of similar shapes constructed on the legs of the triangle. Where: A is the area of the shape on the hypotenuse.

**What does the Pythagorean Theorem say about the areas of the squares on the sides of a right triangle?**

The Pythagorean Theorem can also be represented in terms of area. In any right triangle, the area of the square drawn from the hypotenuse is equal to the sum of the areas of the squares that are drawn from the two legs.

**Do cartographers use the Pythagorean Theorem?**

Surveying. Surveying is the process by which cartographers calculate the numerical distances and heights between different points before creating a map. The Pythagorean Theorem is used to calculate the steepness of slopes of hills or mountains.

## What are the rules of Pythagorean Theorem?

Pythagorean Theorem. The Pythagorean theorem states that in any right triangle, the square of the length of the hypotenuse equals the sum of the squares of the lengths of the legs of the right triangle. This same relationship is often used in the construction industry and is referred to as the 3-4-5 Rule.

**Why does the Pythagorean Theorem need to be squared?**

The squares are required because it’s secretly a theorem about area, as illustrated by the picture proofs you’ve mentioned. Since a side length is a length (obviously), when you square it you get an area.

**How did Pythagoras find the Pythagorean Theorem?**

The legend tells that Pythagoras was looking at the square tiles of Samos’ palace, waiting to be received by Polycrates, when he noticed that if one divides diagonally one of those squares, it turns out that the two halves are right triangles (whose area is half the area of the tile).

### Can the Pythagorean theorem be represented in terms of area?

The Pythagorean Theorem can also be represented in terms of area. In any right triangle, the area of the square drawn from the hypotenuse is equal to the sum of the areas of the squares that are drawn from the two legs. You can see this illustrated below in the same 3-4-5 right triangle.

**What is the Pythagorean theorem for right triangle?**

The Pythagorean Theorem says that, in a right triangle, the square of a (which is a×a, and is written a 2) plus the square of b (b 2) is equal to the square of c (c 2): a 2 + b 2 = c 2 Proof of the Pythagorean Theorem using Algebra

**How do you prove the Pythagorean theorem?**

The Pythagorean Theorem says that, in a right triangle, the square of a (a 2) plus the square of b (b 2) is equal to the square of c (c 2): Proof of the Pythagorean Theorem using Algebra. Take a look at this diagram it has that “abc” triangle in it (four of them actually):

## How to use the Pythagorean theorem to find the hypotenuse?

Note that the Pythagorean Theorem only works with right triangles. You can use the Pythagorean Theorem to find the length of the hypotenuse of a right triangle if you know the length of the triangle’s other two sides, called the legs. Put another way, if you know the lengths of a and b, you can find c.