3 vectors, 3 angles, 1 length?

Question

Okay, i'm completely lost on this question. As much as I know, is that on a 2-d plane, you can find the X and Y component using sin, and cos. Then find the length of the vector using pathagrean theorem. However right now I have a questions saying:

"A ferryboat transports tourists among three islands. It sails from the first island to the second island, 4.94 km away, in a direction 37.0° north of east. It then sails from the second island to the third island in a direction 57.0° west of north. Finally, it returns to the first island, sailing in a direction 28.0° east of south."

But i'm completely lost with how to start it.

Calculate the distance between the second and third islands. and calculate the distance between the first and third islands.
Are what we're supposed to do. But when you have a given value C, and two variables a and b all = 0, it's like 3.8+a+b=0 and doesnt really help me solve it.

Answer 1

You have not said what the question is, but the place to start for any question is to draw a picture. Since you start and end at the same point. the sum of the y components are zero.and the sum of the x components are zero. This give you 2 equations and you have 2 unknown sides.

Edit:
A cos(a) +B cos(b) +C cos (c)=0 x components
A sin(a) +B sin(b) +C sin (c)=0 y components
Vectors with lengths A B C making angles a b c with the x axis

Draw diagram assuming north is in the y direction and figure out angles a b c. You know A so you can use the equations to solve for B and C which are the distanced between islands