Answer:
509.17 ft
Explanation:
We can use the following model to represent the situation when the boat was first noticed.
So, we need to calculate the angle A and the distance x. For angle A, we get:
A = 90° - 16° 18' = 73° 42' =73.7
Now, using the trigonometric function tangent, we can calculate the value of x as follows:
[tex]\begin{gathered} \tan 73.7=\frac{x}{200} \\ 200\times\tan 73.7=x \\ 683.95\text{ ft = }x \end{gathered}[/tex]In the same way, we model the situation when the boat stops as follows:
Therefore, the value of angle B and the distance y are equal to:
B = 90° - 48° 51' = 41° 9' = 41.15°
[tex]\begin{gathered} \tan \text{ 41.15 =}\frac{y}{200} \\ 200\times\tan 41.15=y \\ 174.78\text{ ft = y} \end{gathered}[/tex]Finally, the distance that the boat travel from when it was first noticed until it stopped can be calculated as the distance x less the distance y. So:
x - y = 683.95 ft - 174.78 ft = 509.17 ft
Therefore, the answer is 509.17 ft
