When an engineer inspects a pipeline she notices a high water mark. How much space is there between the high water level and the top of the pipe, to the nearest hundredth.
The diameter of the pipe is 1.2m and the horiztonal distance across the surface of the water is 80 cm.
To find the space between the high water level and the top of the pipe, we can use the concept of a right triangle. Here's how we can calculate it:
1) We know the diameter of the pipe is 1.2m, which means the radius (r) is half of the diameter: r = 1.2m / 2 = 0.6m.
2) Since the horizontal distance across the surface of the water is 80 cm = 0.8m, we can consider this as the base of the triangle.
3) The height of the triangle represents the space between the high water level and the top of the pipe, which we need to find. Let's call it h.
4) Considering the base, height, and hypotenuse of the triangle, we can use the Pythagorean theorem: a^2 + b^2 = c^2.
5) In this case, the base (b) is the known horizontal distance across the surface of the water (0.8m), and the height (a) is the height we want to find (h). The hypotenuse (c) is the radius of the pipe (0.6m).
6) Now we can plug the values into the formula:
0.8^2 + h^2 = 0.6^2
7) Simplifying the equation:
0.64 + h^2 = 0.36
8) Subtracting 0.64 from both sides of the equation:
h^2 = 0.36 - 0.64
h^2 = -0.28
9) Since you can't have a negative value for the height, this means there is no space between the high water level and the top of the pipe. The high water level has reached the top of the pipe.
Therefore, the space between the high water level and the top of the pipe is 0 meters (to the nearest hundredth).