Real-Life Applications of The Pythagoras Theorem

Kush Gupta                 X-G                   Roll No. 16

Real-Life Applications of The Pythagoras Theorem

Pythagorean Theorem is one of the most fundamental theorems in mathematics and it defines the relationship between the three sides of a right-angled triangle. It is the triangle with one of its angles as a right angle, that is, 90 degrees. The side that is opposite to the 90-degree angle is known as the hypotenuse. The other two sides that are adjacent to the right angle are called the legs of the triangle.

The foremost question: What is the Pythagorean Theorem??

The Answer: The Pythagorean theorem states that the sum of the squares of the legs of a right triangle equals the square of its hypotenuse, that is, a2 + b2 = c2, as shown in the figure below.

Numbers whose values satisfy the Pythagorean theorem, such as 3, 4, and 5(32 + 42 = 9 + 16 = 25 = 52), are known as Pythagorean triplets (permissible values for the sides of a right triangle). All triplets lead to triangles having a hypotenuse that is one unit longer than the larger leg. 

The Pythagorean theorem is used to find the sides of a right-angled triangle. This theorem is mostly used in Trigonometry, where we use trigonometric ratios such as sine, cos, and tan to find the length of the sides of the right triangle.

 

5 Real-Life Applications of The Pythagorean Theorem

1. Architecture

The Pythagorean Theorem is applicable to calculate the length of the diagonal connecting any two straight lines. This aspect of the Pythagorean theorem is pretty useful in designing and construction. For instance, while building a sloped roof, if you know the height and the length of the roof to cover, you can use the Pythagorean Theorem to find the diagonal length or to calculate the roof’s slope. You can utilize this data to precisely cut beams to support the roof structure or to calculate the roof’s total area.

2. Navigation

The Pythagorean theorem is useful in two-dimensional navigation, mostly used by ships to find the shortest routes. Sailors navigate using this theorem by making a horizontal and a vertical line from the current location to form a right triangle in order to find the shortest distance to the destination. The distances in each direction will be the two sides of the triangle, and the shortest line connecting them will be diagonal. The same law applies to other forms of navigation on land or in the sky. For instance, a flight can use its altitude above sea level and its distance from the destination airport to find the exact geolocation to begin a safe descent to that airport.

3. Design and Construction

Square shapes and right angles are frequently used in building plans and construction work. The Pythagoras theorem’s fundamental property, which states that a triangle will always have a right angle if its sides meet the condition, is used by engineers for this purpose.

 For example, Television and Computer Screens

The size of TVs and monitors is always specified in terms of diagonal. If a television is specified as 32 inches in size, its size is the diagonal measurement, known as the hypotenuse.

4. Surveying

Surveying is the process by which cartographers calculate the numerical distances and heights between different points before creating a map. Because the terrain is often uneven, surveyors must find ways to take measurements of distance in a systematic way. The Pythagorean Theorem is used to calculate the steepness of slopes of hills or mountains. A surveyor looks through a telescope toward a measuring stick a fixed distance away, so that the telescope's line of sight and the measuring stick form a right angle. Since the surveyor knows both the height of the measuring stick and the horizontal distance of the stick from the telescope, he can then use the theorem to find the length of the slope that covers that distance, and from that length, determine how steep it is.

5. Pythagoras Theorem In A Security Camera

Nowadays face recognition becomes very important in security areas and it reduces the turmoil in an investigation of a crime. The concept of Pythagoras theorem is helpful to calculate the distance between the position of the camera and the place where the crime is noted and it is also helpful to set the angle for face recognition in security cameras.