Question

mr. miller’s field of vision from his beach house is 140 degrees and he can see ships on the horizon up to 4 miles away. the diagram below. mr. miller’s field of vision horizon? r = 4 miles 140° mr. miller’s position which measurement is closest to how many miles mr. miller can see along the arc of his field of vision? 9.8 miles 19.5 miles 25.1 miles 12.6 miles

Explanation:

Step1: Recall arc length formula

The formula for arc length $s$ is $s = \frac{\theta}{360^\circ} \times 2\pi r$, where $\theta$ is the central angle, and $r$ is the radius.

Step2: Substitute given values

Given $\theta = 140^\circ$, $r = 4$ miles.
$
s = \frac{140^\circ}{360^\circ} \times 2\pi \times 4
$

Step3: Simplify the expression

First simplify $\frac{140}{360} = \frac{7}{18}$, then calculate $2\times4=8$:
$
s = \frac{7}{18} \times 8\pi = \frac{56\pi}{18} \approx \frac{56\times3.1416}{18} \approx 9.8
$

Answer:

9.8 miles