Question

reed is snorkeling on the surface of the ocean, 22 feet from an anchored boat. the anchor is on the ocean floor, 34 feet away from reed. what is the angle of depression between reed and the anchor

Answer 1

To find the angle of depression from Reed to the anchor, we can model the situation as a right triangle.

1. **Identify the Triangle:**
- The horizontal distance from Reed to the boat is 22 feet (this will be one leg of the triangle).
- The vertical distance from Reed to the anchor (down to the ocean floor) is 34 feet (this will be the other leg of the triangle).

2. **Determine the Hypotenuse:**
- The distance from Reed to the anchor can be calculated using the Pythagorean theorem:
\[
c = \sqrt{(22)^2 + (34)^2}
\]
- Calculate \(c\):
\[
c = \sqrt{484 + 1156} = \sqrt{1640} \approx 40.5 \text{ feet}
\]

3. **Calculate the Angle of Depression:**
- The angle of depression (let's call it \(θ\)) can be found using the tangent function:
\[
\tan(θ) = \frac{\text{opposite}}{\text{adjacent}} = \frac{34}{22}
\]
- To find the angle \(θ\), take the arctangent:
\[
θ = \tan^{-1}\left(\frac{34}{22}\right)
\]

4. **Using a calculator:**
- Calculate \(θ\):
\[
θ \approx \tan^{-1}(1.545) \approx 57.5^\circ
\]

Therefore, the angle of depression from Reed to the anchor is approximately **57.5 degrees**.