To find the angle of depression between Reed and the anchor, we can use the information given to identify a right triangle formed by Reed, the anchor, and the point directly beneath Reed on the ocean floor.
In this case, we have:
- The distance from Reed to the boat (horizontal distance) is 22 feet.
- The distance from the boat to the anchor (the hypotenuse of the right triangle) is 34 feet.
We can use the Pythagorean theorem to first find the vertical distance (d) from Reed to the ocean floor (the anchor). The relationship is:
\[ d^2 + 22^2 = 34^2 \]
Calculating this gives us:
\[ d^2 + 484 = 1156 \] \[ d^2 = 1156 - 484 \] \[ d^2 = 672 \] \[ d = \sqrt{672} \approx 25.9 \text{ feet} \]
Now, we can find the angle of depression (\( \theta \)) using the tangent function:
\[ \tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} = \frac{d}{22} = \frac{25.9}{22} \]
Calculating this:
\[ \tan(\theta) \approx 1.176 \]
Now, we find the angle \( \theta \):
\[ \theta \approx \tan^{-1}(1.176) \approx 50.2° \]
Therefore, the closest angle from the responses is:
50°