Let's note the distance from the helicopter to the nearest foot of the island as \(x\). We can create a right triangle with the helicopter at the top, point P on the island, and the foot of the island forming the right angle.
In a right triangle, the tangent function relates the angle of depression to the sides of the triangle. The tangent of the angle of depression is equal to the length of the opposite side (distance from the helicopter to the foot of the island) divided by the length of the adjacent side (distance from the helicopter to point P).
Using the tangent function, we have:
\(\tan(33°) = \frac{x}{600}\)
To find \(x\), we can rearrange the equation:
\(x = \tan(33°) \cdot 600\)
we can find the value of \(\tan(33°)\) to be approximately 0.6494. Plugging this value into the equation:
\(x = 0.6494 \cdot 600\)
Calculating the result:
\(x \approx 389.64\)
Therefore, the nearest foot of the island is approximately 389.64 feet off the coast.