1. The problem is to explain the equation used in surveying, which often involves calculating distances, angles, or elevations. 2. A common surveying equation is the distance formula between two points: $$d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$$ where $(x_1, y_1)$ and $(x_2, y_2)$ are coordinates of two points. 3. This formula comes from the Pythagorean theorem, which relates the sides of a right triangle. 4. To use it, subtract the coordinates of the points to find the differences in $x$ and $y$. 5. Square these differences, add them, and then take the square root to find the distance. 6. For example, if point 1 is at $(3,4)$ and point 2 is at $(7,1)$, then: $$d = \sqrt{(7 - 3)^2 + (1 - 4)^2} = \sqrt{4^2 + (-3)^2} = \sqrt{16 + 9} = \sqrt{25} = 5$$ 7. This means the distance between the two points is 5 units. 8. Surveying also uses angles and trigonometry, but this distance formula is fundamental for calculating straight-line distances on a plane. This explanation covers the basic surveying distance equation and how to apply it.