To determine how far below Levi the hook is, we can represent the situation using the right triangle formed by Levi, the fish, and the hook. Let's denote:
- Levi's position as point \( L \)
- The fish's position as point \( F \)
- The position of the hook as point \( H \)
According to the problem, we have:
- The horizontal distance between Levi and the fish \( LF = 89 \) feet.
- The horizontal distance from the fish to the hook \( FH = 39 \) feet.
Let \( d \) be the vertical distance from Levi down to the hook (i.e., the depth of the hook). Because Levi is above the hook and the fish is at the same depth as the hook, we can represent the triangle as follows:
- The distance \( LH \) (the straight distance from Levi to the hook) can be derived from the Pythagorean theorem using the horizontal distance \( LF \) and the vertical distance \( d \):
\[ L H^2 = L F^2 + F H^2 \]
Which can be expressed as:
\[ d^2 + 39^2 = 89^2. \]
Calculating \( 39^2 \) and \( 89^2 \):
\[ 39^2 = 1521, \] \[ 89^2 = 7921. \]
Putting these values into the equation:
\[ d^2 + 1521 = 7921. \]
Now, subtract 1521 from both sides to find \( d^2 \):
\[ d^2 = 7921 - 1521 = 6400. \]
Finally, take the square root to find \( d \):
\[ d = \sqrt{6400} = 80. \]
So, the hook is 80 feet below Levi.
Final Answer: 80 feet.