Trig with Vectors

[SlittyEyes]

I'm having a lot of trouble with the wording. I tried with the interpretation I think is right, but keep coming up with the wrong answer.

On a hiking trip, you start at point A and hike 5 miles in a direction that’s 4° north of due east. Then, you turn your path slightly, by 10° to your right, and walk until you are directly east of point A where you started.
a. Draw a diagram of the situation. How long do you have to hike in this new direction before you make it back onto your intended trail?
b. How much shorter would your path have been, if you just walked straight east instead of up and then down?

Here's what I have so far:

 

[SlittyEyes]

64 a 3.34 miles approx.
64 b 0.03 miles

No, I haven't learned the Law of Sines

 

[SlittyEyes]

Thanks! I kept doing it over and over again, didn't realize that i was right and that there was a typo in the answer key. I used the law of sines and came up with about a 5 mile difference between the two paths.