A fisherman used a 12 foot rope to tie a boat to the dock. The rope makes an angle of 40 degrees with the ocean. How far is the boat from the dock?

x/12 = cos40

9.19 To find the distance between the boat and the dock, we can use trigonometry. Specifically, we can use the sine function since we know the length of the rope and the angle it makes with the ocean.

Here's how you can find the distance:

1. Identify the given values:
- Length of the rope: 12 feet
- Angle between the rope and the ocean: 40 degrees

2. Recall the definition of the sine function: sin(theta) = opposite/hypotenuse. In this case, the opposite side is the distance between the boat and the dock, and the hypotenuse is the length of the rope.

3. Rearrange the equation to solve for the distance:
- sin(40 degrees) = distance/12 feet

4. Solve the equation for the distance:
- distance = 12 feet * sin(40 degrees)
- Use a calculator to find the value of sin(40 degrees), and multiply it by 12 feet.

By following these steps, you can calculate the distance between the boat and the dock.