As it passes over Grand Bahama Island, the
Eye of a hurricane is moving in a direction 69◦
North of west with a speed of 37 km/h. Three
Hours later, it shifts due north, and its speed
Slows to 98 km/h.
How far from Grand Bahama is the eye 4.50
H after it passes over the island? Answer in
Units of km.

A weird question... Is this a Projectile motion??

Start with a dot that represents the Grand Bahama Island. Draw a line at 69 degrees northwest. This makes a 69 degree angle with north. The length of the line is 3 * 37 (37 kph * 3 hrs = 111 kilometers). From there, draw a line due north. The length of this line is (4.5 - 3) = 1.5 hours * 98 kph = 147 kilometers long.

Now the question I have, is if it starts at 37 km/h, how can it "slow" to 97 km/h?

In any case, you have two lines. The third line back to the Grand Bahama is the length that you need.

I've created an attachment that shows the situation. Call the Grand Bahama point G.

Construct a triangle AGD by drawing a line due east of point A.
You know the angle DGA and you know the length of the GA line, so you can solve the ADG triangle.

The length of BA is the same as CD. And AD is the same length as BC. You just solved for DG so you can add that to CD and get the length of the side of the GC triangle. You now know BC and CG so you can calculate the angle BGC and solve the entire triangle.

I have never attacned a file to one of these posts, so I hope this works.

Hope this is a reasonable explanation.