Question
Demetry is deep-sea fishing. They have a device that tells them the diagonal distance from their boat to the fish, and how far down the fish is under the water. If the device tells them there is a fish 109 feet down and 230 feet away from them, what is the approximate angle they’ll need to get their fishing line to catch the fish?(1 point) Responses 28° 28° 46° 46° 62° 62° 90°
Answers
GPT-4o mini
To find the angle at which Demetry needs to lower the fishing line to catch the fish, we can use trigonometry. Specifically, we can use the tangent (tan) function, which is defined as the opposite side over the adjacent side in a right triangle.
In this scenario:
- The depth of the fish (the opposite side) is 109 feet.
- The horizontal distance to the fish (the adjacent side) is 230 feet.
Using the tangent function:
\[
\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} = \frac{109}{230}
\]
To find the angle \(\theta\), we take the arctangent (inverse tangent) of the ratio:
\[
\theta = \tan^{-1}\left(\frac{109}{230}\right)
\]
Now we can calculate this value:
\[
\theta \approx \tan^{-1}(0.4739) \approx 25.0^\circ
\]
Since the answer choices given do not include the exact angle we calculated, we can check the available options. The closest option to 25° is 28°, which appears to be the best approximation. Thus, the answer to the question would be **28°**.
In this scenario:
- The depth of the fish (the opposite side) is 109 feet.
- The horizontal distance to the fish (the adjacent side) is 230 feet.
Using the tangent function:
\[
\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} = \frac{109}{230}
\]
To find the angle \(\theta\), we take the arctangent (inverse tangent) of the ratio:
\[
\theta = \tan^{-1}\left(\frac{109}{230}\right)
\]
Now we can calculate this value:
\[
\theta \approx \tan^{-1}(0.4739) \approx 25.0^\circ
\]
Since the answer choices given do not include the exact angle we calculated, we can check the available options. The closest option to 25° is 28°, which appears to be the best approximation. Thus, the answer to the question would be **28°**.