This problem. We have a fisherman who is standing longshore here. Okay? He has ah, hooked a trout, and he is reeling in the fishing line. Okay, The tip of his rod. Hey, his rod is perfectly vertical, and this is 12 feet tall. Okay, so we are going to label this, um, are for Rod. Okay, then here is our line, and our line is being reeled in. Hey, at a rate off four inches per second and the fish is being pulled this direction. So we're gonna call this F for fish. All right. So we know D L D t is negative. Four inches per second because it's the, um, length is decreasing. Okay. What we want to find is what is g f d t. When the fish is 20 feet from the shore. All right, so let's look here. Looks to me like we have a right triangle. So we're gonna work with the Pythagorean theorem. We have asked Squared plus R squared is equal to l squared. Okay. In this instance, we do have a constant the rod. The length of that raw never changes so we can go ahead and put 12 in for our huh? Now we're going to differentiate this equation with respect to time, so we're gonna have to f d F d t plus well, the derivative of a constant zero. Okay, so that doesn't even need to be there. So that's gonna be equal to two. L d l d t. All right, I'm gonna go ahead and cross off my choose because I'm just going to divide the entire equation by two. So I'm gonna substitute in what I know. So we want to know at 20 feet how fast the fish is being pulled in. So twenties we're gonna plug in for F, and we're solving for the f D. T el is Well, we gotta figure out l So let's come over here to the side and we'll do another path. Angry. And Vera, this time we're gonna put 20 in, we're at, and we're solving for l. All right, so let's look here. We're going to have if we swear 20 and square 12 and add them together. We have 544 and the square root of 544 is 23.32. So l is going to be 23.32 An de L D. T is negative four inches 1st 2nd but we're talking about feet for the distance of the fish. So let's convert this two feet per second. So four inches would be 1/3 of a foot, so negative one their word feet per second. All right, now we can go ahead and do some calculating. Here we have 23.32 times negative. 1/3 is gonna give us negative 7.77 Divide out the 20 from both sides and we have negative 0.3885 feet per second. And if you want that in inches, it would be 4.66 inches per second. Hey, that would be negative. And all the negative tells us is that the distance from the fish to the man is decreasing.