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?(1 point)
Responses

50°
50 degrees

65°
65 degrees

90°
90 degrees

40°

Answer 1

To find the angle of depression from Reed to the anchor, we can use the information given about the distances:

1. The horizontal distance from Reed to the boat (on the surface) is 22 feet.
2. The distance from Reed vertically down to the anchor is 34 feet.

We can visualize this situation as a right triangle where:
- The horizontal leg is 22 feet (distance from Reed to the boat).
- The vertical leg is 34 feet (depth of the anchor).

We can find the angle of depression (θ) using the tangent function, which is the opposite side (depth) over the adjacent side (horizontal distance):

\[
\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} = \frac{34}{22}
\]

Now, let's calculate \(\theta\):

\[
\theta = \tan^{-1}\left(\frac{34}{22}\right)
\]

Calculating this gives:

\[
\theta \approx \tan^{-1}(1.5455)
\]
\[
\theta \approx 57.7°
\]

Since 57.7° is not one of the options given, the closest angle in the provided choices is:

65°

So the best response based on the options provided is:

65°