To determine how far Betty is from the fish, we can visualize the situation as a right triangle.
- The depth of the hook (and the fish) is 7 meters below the surface. This represents the vertical distance from Betty's boat to the depth where both the hook and the fish are located.
- The horizontal distance from the point directly below the boat to the fish is given as 6 meters.
We can use the Pythagorean theorem to find the distance between Betty and the fish. In a right triangle, the theorem states:
\[ c^2 = a^2 + b^2 \]
where:
- \( c \) is the hypotenuse (the straight-line distance between Betty and the fish),
- \( a \) is the vertical distance (7 meters),
- \( b \) is the horizontal distance (6 meters).
Now, we substitute the values:
\[ c^2 = 7^2 + 6^2 \] \[ c^2 = 49 + 36 \] \[ c^2 = 85 \]
Next, we take the square root to find \( c \):
\[ c = \sqrt{85} \approx 9.22 \]
Rounding to the nearest tenth, the distance from Betty to the fish is approximately:
\[ \boxed{9.2} \text{ meters} \]
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