Question

Square Roots Discussion Required Resources Read/review the following resources for this activity: OpenStax Textbook Readings Lesson in Canvas Assignments in Knewton Understanding Square Roots Simplifying Square Root Expressions Multiplying Square Root Expressions Dividing Square Root Expressions Adding and Subtracting Square Root Expressions Triangles and the Pythagorean Theorem Solving Radical Equations Initial Post Instructions One of the most famous formulas in mathematics is the Pythagorean Theorem. It is based on a right triangle,and states the relationship among the lengths of the sides as a2 b2= c2, where a and b refer to the legs of a right triangle and c refers to the hypotenuse. It has immeasurable uses in engineering, architecture, science, geometry, trigonometry, algebra, and in everyday applications. For your first post, search online for an article or video that describes how the Pythagorean Theorem can be used in the real world. Provide a one paragraph summary of the article or video in your own words. Be sure you cite the article and provide the link.

Answer 1

The Pythagorean theorem expresses the relationship between the sides of a right-angled triangle. It is frequently used to calculate distances or solve problems in various fields like construction, navigation and surveying.

Step-by-step explanation:

The Pythagorean theorem is a fundamental principle in geometry that establishes a relationship between the sides of a right-angled triangle. The theorem, which can be expressed as a² + b² = c², implies that the square of the hypotenuse (side c) is equal to the sum of the squares of the other two sides (a and b).
This equation can be reorganized to solve for the hypotenuse by taking the square root of both sides, resulting in c = √(a² + b²). This theorem has many practical applications in real life.

For example, it can be used to calculate the straight-line distance between two points when the individual distances east/west and north/south are known, to design right-angled components in engineering and construction, and to solve problems in navigation and surveying.

Furthermore, should one need to find the length of one of the legs when the hypotenuse and the other leg's lengths are known, it's a matter of 'undoing' the square—extracting the square root. By rearranging the theorem, we get a² = c² - b² and hence a = √(c² - b²), allowing us to solve for the unknown side length.