a boat travels on a course of bearing n 37 10' W for 79.5 miles. How many miles north and how many miles west has the boat traveled?

79.5cos37.17 = 63.4 miles north

79.5sin37.17 = 48.0 miles west

To determine the number of miles north and west the boat has traveled, you need to understand how bearings work and how to use trigonometry to calculate the distances.

First, let's break down the given information:
- The boat is traveling on a bearing of N 37°10'W.
- The boat has traveled a distance of 79.5 miles.

Now, when we say a bearing of "N 37°10'W," it means that the boat is heading 37°10' west of north.

To find the distance north and west, we can use trigonometry. We'll create a right-angled triangle with the boat's path as the hypotenuse, the angle between north and the boat's path as the angle, and the distances north and west as the two other sides.

Now, let's calculate the distances.

Step 1: Convert the bearing to decimal degrees.
To convert the minutes (') to decimal degrees, divide the minutes by 60.
37°10' / 60 = 0.6183°

Step 2: Calculate the distance north:
The distance north can be found using trigonometry. We can use the sine function since the opposite side is the distance north, and the hypotenuse is the distance traveled (79.5 miles).
sin(angle) = opposite / hypotenuse
sin(0.6183°) = distance north / 79.5 miles

To find the distance north: distance north = sin(0.6183°) * 79.5 miles

Step 3: Calculate the distance west:
The distance west can be found using trigonometry as well. We can use the cosine function since the adjacent side is the distance west, and the hypotenuse is 79.5 miles.
cos(angle) = adjacent / hypotenuse
cos(0.6183°) = distance west / 79.5 miles

To find the distance west: distance west = cos(0.6183°) * 79.5 miles

By plugging in the values into the equations and calculating them, we can find the distances north and west traveled by the boat.

d = 79.5mi[N37o 10'W] = 79.5mi[127.17o]

CCW.

X = 79.5*Cos127.17 = Miles west.
Y = 79.5*sin127.17 = Miles north.

Those answers are wrong