(Solved): An angler hooks a trout and reels in his line at \( 5 \mathrm{in.} / \mathrm{s} \). Assume the tip ...

An angler hooks a trout and reels in his line at \( 5 \mathrm{in.} / \mathrm{s} \). Assume the tip of the fishing rod is \( 13 \mathrm{ft} \) above the water and directly above the angler, and the fish is pulled horizontally directly toward the angler (see figure). Find the horizontal speed of the fish when it is \( 22 \mathrm{ft} \) from the angler. Let \( x \) be the horizontal distance from the angler to the fish and \( z \) be the length of the fishing line, where both \( x \) and \( z \) are measured in inches. Write an equation relating \( x \) and \( z \). \[ x^{2}+132^{2}=z^{2} \] Differentiate both sides of the equation with respect to \( \mathrm{t} \). \[ (2 x) \frac{d x}{d t}=(2 z) \frac{d z}{d t} \] When the fish is \( 18 \mathrm{ft} \) from the angler, its horizontal speed is about (Round to two decimal places as needed.)