To find the angle of depression between Reed and the anchor, we can use the information given to visualize a right triangle. In this triangle:
- The distance from Reed to the boat (22 feet) is one leg of the triangle (horizontal leg).
- The distance from the boat to the anchor (34 feet) is the hypotenuse.
- The vertical distance from the surface of the ocean to the anchor can be calculated using the Pythagorean theorem.
First, let's denote:
- \(a = 22\) feet (horizontal distance from Reed to the boat),
- \(c = 34\) feet (hypotenuse from the surface to the anchor).
We can find the vertical distance \(b\) (depth to the anchor) using the Pythagorean theorem: \[ a^2 + b^2 = c^2 \] \[ 22^2 + b^2 = 34^2 \] \[ 484 + b^2 = 1156 \] \[ b^2 = 1156 - 484 \] \[ b^2 = 672 \] \[ b = \sqrt{672} \approx 25.9 \text{ feet} \]
Now, we want to find the angle of depression. The angle of depression \(θ\) can be calculated using the tangent function: \[ \tan(θ) = \frac{\text{opposite}}{\text{adjacent}} = \frac{b}{a} \] So, \[ \tan(θ) = \frac{25.9}{22} \]
Calculating this: \[ \tan(θ) \approx 1.176 \]
Now, to find the angle \(θ\): \[ θ = \tan^{-1}(1.176) \approx 50.2° \]
Hence, rounding to the nearest whole number, the angle of depression is approximately 50°.
Therefore, the answer is: 50°