Describe one useful application of the Pythagorean theorem?
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One useful application of the Pythagorean theorem is in calculating the distance between two points in a two-dimensional plane, such as in navigation or mapping. The Pythagorean theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
To apply the Pythagorean theorem, we can use the following steps:
1. Identify the two points between which you want to calculate the distance. Let's call them point A and point B.
2. Determine the coordinates of each point. For example, point A may have coordinates (x1, y1), and point B may have coordinates (x2, y2).
3. Use the formula for calculating distance using the Pythagorean theorem: distance = sqrt((x2 - x1)^2 + (y2 - y1)^2).
4. Plug the coordinates from step 2 into the formula and calculate the difference in the x-coordinates (x2 - x1) and the difference in the y-coordinates (y2 - y1).
5. Square both differences and add them together.
6. Take the square root of the sum to obtain the distance between point A and point B.
By applying the Pythagorean theorem, we can find the straight-line distance between two points on a plane, which is valuable in various fields such as geometry, physics, engineering, and navigation.