How Do You Calculate Distances Between Islands Using Vector Components?

[kbump]

Homework Statement

A ferryboat transports tourists among three islands. It sails from the first island to the second island, 4.02 km away, in a direction 37.0° north of east. It then sails from the second island to the third island in a direction 69.0° west of north. Finally, it returns to the first island, sailing in a direction 28.0° east of south. (a) Calculate the distance between the second and third islands. (b) Calculate the distance between the first and third islands.

Homework Equations

The Attempt at a Solution

Sadly, I don't know where to start. I know I have to find the x and y components, but don't know how since only one side/distance is given. Any help is appreciated..

 

[rock.freak667]

Do you the answers to the question? i got for part a)5.153km if that is correct then i shall help you get out part b)

 

[bob1182006]

I tried but got 5.79 km for part a.

The way I did it:

draw a diagram.

start with the first island, approximate 37 degrees N of E, and do the rest to all the other islands.

Now extend the N/S/E/W lines @ each of the islands. You should get triangles starting to appear. you know 2 of the angles. from the starting island you have 37 degrees, and the right angle of the triangle. So you can find the other angle and from there you can find all other angles.

You can then find the 3 angles within the "triangle" that the ship takes along the islands. You know 1 side 1->2nd island. Use the law of sines A/sin(a) = B/sin(b) = C/sin(c) and you can find all of the distances.

 

[rock.freak667]

Well that is the same way i got my answer, although i most likely made some error in my diagram

 

[kbump]

I don't get the solution. It's actually online, so I type my answer and it let's you know if it was correct. I actually tried the same method and got 24, 107, and 49 for my angles, but didn't know where to go from there. I tried typing in 5.79 for part a and it was incorrect. I only have one more shot at it, so I want to make sure it's right and I know what I'm doing before I submit again.

 

[P.O.L.A.R]

Ok I think I have the trick is to draw it out an use the law of sine a/sin(A)=b/sin(B)=c/sin(C) for part a i got 6.83km much diff than the rest. You have to place the angle across from the side like the picture.
http://www.elderhs.net/staff/knepflecc/law_of_sines_cosines/triangle_for_sine_area_formula.gif

 

[Yapper]

My diagram( very rough) is attached, my angles are 41, 58, 81. And I got 6.05km for my answer,