When we deploy an acoustic mooring, we start with the buoy (the big yellow top float) first. Then we attach more wire and instruments as the ship slowly moves forward. By the time we're ready to attach the anchor, we have about 3.5 miles of wire strung out behind the ship. The last step in the deployment is to dump the anchor and let it sink to the bottom. The anchor pulls the rest of the mooring underwater.
We let go of the anchor at our chosen site, but the anchor doesn't fall straight to the bottom because it's being dragged back by the buoy and other equipment on the 3.5 mile wire. After the anchor has reached the bottom (it takes about 50 minutes), we have to do a survey to figure out exactly where it landed.
Naturally, we use acoustics to do the survey. Similar to how we measured the bottom depth, we send a short "ping" from the ship to the anchor. The acoustic release (a piece of equipment attached the anchor) replies with another ping. By measuring the time it takes for this signal to travel to the bottom and back, we can figure out how far away the anchor is from the ship. The picture below shows what we might learn from making one distance measurement:
A single distance measurement tells us that the anchor could lie anywhere on that blue circle. (The distance from the ship to any point on the circle is the same.) Since we need to know the exact anchor position, we obviously have to make some more measurements. So we move the ship and make a second measurement of the travel time (thus the distance) to the anchor. The picture below shows us what that second measurement tells us:
Now we know that the anchor has to lie on both the blue and the red circles. That means that the anchor could be at one of two places (indicated by the stars on the plot). Taking a second measurement obviously narrowed down the list of possible locations for the anchor. Let's see what happens when we take a third measurement:
Now the anchor has to lie on all three circles, so we know it must be located at the intersection point (marked with a triangle). Hooray! We've found our anchor!
As you can see from this post, acoustic surveys require knowing a bit of geometry (to find the intersection points of these circles). It's a practical application of the mathematics you have learned (or will learn) in school.