Confusion about physics vectors in question

[x86]

Homework Statement

Engineers perform a crash test with a minivan and a compact car. The mass of the minivan is 800kg and the mass of the compact car is 560kg. The minivan was moving north, and the compact was was moving east.
After the collision, the two cars crumpled together and moved at 15m/s [N 30 E]. Determine the initial velocity of each vehicle

Homework Equations

P = mv

The Attempt at a Solution

Okay so its inelastic:
Minivan is 1
Compact car is 2

x:
m1v1 + m2v2 = mtvf
m2v2 = mtvf
560 * v2 = (560+800)(15*cos70)
v2 = 12.45 m/s [E]

y:
m1v1 + m2v2 = mtvf
800*v2 = (560+800)(15*sin70)
v2 = 24 m/s [N]

The confusion is that these answers are wrong. The book gets completely different answers, and I've discovered its because the book does it like this
How the book is doing it
x:
m1v1 + m2v2 = mtvf
m2v2 = mtvf
560 * v2 = (560+800)(15*sin30)
v2 = 18 m/s [E]

y:
m1v1 + m2v2 = mtvf
800*v2 = (560+800)(15*cos30)
v2 = 22 m/s [N]

This is so confusing for me. Why is the book using sin30 where I use cos70, and why is the book using cos30 where I am using sin70?

I drew the triangle, and I just can't understand why the book is doing it like this. Can someone clear this up? Thanks

I realize this is a trigonometry question. But why isn't sin70 equal to cos30 in the triangle I am drawing? Whats going on?

 

[jedishrfu]

sin 70 is equivalent to cos 20 not cos 30

sin 60 is equivalent to cos 30

angles must add to 90 not 100

 

[x86]

sin 70 is equivalent to cos 20 not cos 30

sin 60 is equivalent to cos 30

angles must add to 90 not 100

Thank you, solves all my problems. I fail at math today. I was thinking 70 + 30 = 90.

 

[voko]

Perhaps you should first explain where your 70 degree measure came from, if the only angle mentioned in the problem is 30 degree.

 

[x86]

Perhaps you should first explain where your 70 degree measure came from, if the only angle mentioned in the problem is 30 degree.

Everything is solved now, but what I did was I transformed the triangle and set 70 degrees as theta. It should have been 60 degrees, but I wasn't using a calculator so I assumed 90-30 was 70 for some reason