Question

watch the video and then solve the problem given below. click here to watch the video. a boat leaves the entrance to a harbor and travels 125 miles on a bearing of n 50° e. how many miles north and how many miles east from the harbor has the boat traveled?

Explanation:

Step1: Define the components

We can use trigonometry. Let the distance traveled north be $y$ and the distance traveled east be $x$. The distance traveled by the boat $d = 125$ miles and the angle $\theta=50^{\circ}$.

Step2: Calculate the north - ward distance

The north - ward distance $y$ is given by $y = d\cos\theta$. Substituting $d = 125$ miles and $\theta = 50^{\circ}$, we have $y=125\cos(50^{\circ})\approx125\times0.6428 = 80.35$ miles.

Step3: Calculate the east - ward distance

The east - ward distance $x$ is given by $x = d\sin\theta$. Substituting $d = 125$ miles and $\theta = 50^{\circ}$, we have $x = 125\sin(50^{\circ})\approx125\times0.7660=95.75$ miles.

Answer:

The boat has traveled approximately 80.35 miles north and 95.75 miles east.