use the Pythagorean theorem to find the missing length: one side is 4 in, the other side is 9 in, it is a right triangle
formaula for the Pythagorean theorem
The formula for the Pythagorean theorem is as follows:
c^2 = a^2 + b^2
In this formula, "c" represents the length of the hypotenuse (the side opposite the right angle), while "a" and "b" represent the lengths of the other two sides (legs) of the right triangle.
when can u use the pythagorean theorem
when can u use the pythagorean theorem in the real world
The Pythagorean theorem has various real-life applications, as it relates to the relationship between the sides of right triangles. Here are a few examples:
1. Construction and Architecture: Architects and engineers use the Pythagorean theorem to ensure the stability and integrity of structures. It helps in determining the lengths of diagonal support beams, the height of buildings, or the diagonal distance between corners of rectangular structures.
2. Navigation and Surveying: The Pythagorean theorem is fundamental in navigation and surveying. It is used to calculate distances, especially when measuring short, direct distances between two points, such as the crow-fly distance between two landmarks on a map.
3. Physics: The theorem is utilized in physics to analyze the motion and forces acting on objects. For instance, when calculating the net displacement of an object moving at an angle or the components of a force acting on an object.
4. Technology and Electronics: The Pythagorean theorem is used in various technological applications. It helps in determining the screen size of TVs, monitors, and mobile devices, as well as optimizing the placement of speakers and sound systems to achieve better sound balance and dispersion.
These are just a few examples, but the Pythagorean theorem has far-reaching applications in diverse fields such as astronomy, computer graphics, sports, and more. Its geometric principles have proven to be highly valuable in solving practical problems.
The Pythagorean theorem can be used to solve for the length of one side of a right triangle when the lengths of the other two sides are known. In other words, it can be used to find the missing side length in a right triangle.
The theorem states that the sum of the squares of the lengths of the two legs (the sides adjacent to the right angle) is equal to the square of the length of the hypotenuse (the side opposite the right angle).
So, if you have a right triangle and you know the lengths of two of its sides, you can use the Pythagorean theorem to find the length of the third side.
To use the Pythagorean theorem, we can denote the missing length as "c", and the given sides as "a" and "b". According to the theorem, the sum of the squares of the two legs (a and b) is equal to the square of the hypotenuse (c).
Using the information in the problem, we have:
a = 4 in
b = 9 in
We can now use the formula:
c^2 = a^2 + b^2
Substituting the given values:
c^2 = 4^2 + 9^2
c^2 = 16 + 81
c^2 = 97
To find the missing length "c", we take the square root of both sides:
√c^2 = √97
c = √97
Therefore, the missing length is approximately equal to √97 inches.