Answer:
The boat has traveled 107.7 miles north
The boat has traveled 137.9 miles east
Explanation:
If the boat travels 175 miles on a bearing of N 52° E, we can represent the situation as follows
So, it forms a right triangle and we can use the trigonometric functions to know how much it travels north and east.
Since the north distance is the adjacent side of the given angle, we get
[tex]\begin{gathered} \text{cos}52=\frac{\text{Adjacent}}{Hypotenuse} \\ \cos 52=\frac{y}{175} \\ 175\cdot\cos 52=y \\ 175(0.62)=y \\ 107.7\text{ mil}es\text{ = y} \end{gathered}[/tex]
Then, the boat has traveled 107.7 miles north
In the same way, the distance to the east is the opposite side, so
[tex]\begin{gathered} \sin 52=\frac{Opposite}{Hypotenuse} \\ \sin 52=\frac{x}{175} \\ 175\cdot\sin 52=x \\ 175(0.79_{})=x \\ 137.9\text{ miles = x} \end{gathered}[/tex]
So, the boat has traveled 137.9 miles east
