What did I do wrong in finding the resultant of these vectors?

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I have to find the resultant of:

[PLAIN]http://img17.imageshack.us/img17/8263/68709011.jpg

So I decided to break it up into components:

[PLAIN]http://img37.imageshack.us/img37/7032/71250823.jpg

(The black arrow in the first picture is the blue arrow in the second, that's the way I did it!)

I found the blue line in the picture using the cosine rule:

c \ = \ \sqrt{30^2 \ + \ 40^2 \ - \ (2 \cdot 30 \ \cdot \ 40 \ \cdot \ \cos(120))

c = 60.827 and it's just horizontal along the x-axis.

Then I added c = 60.827 to the third vector:

[PLAIN]http://img96.imageshack.us/img96/1917/92586648.jpg

I found the white arrow, the total resultant, using the same technique:

d \ = \ \sqrt{25^2 \ + \ 60.827^2 \ - \ (2 \cdot 25 \ \cdot \ 60.827 \ \cdot \ \cos(105))

d = 71.5

My book says the answer is 67.6

I got the angle of the resultant using the sine rule:

\theta \ = \ \sin^{-1} ( \frac{25 \cdot \sin(105)}{60.827} ) \ = \ 23.39

My book says the angle is: 11.3°

What did I do wrong?

 

[Mindscrape]

Where did you get 105? Clearly the most straightforward way to do this is to break it up into components, i.e. x=30cos45+40cos15+25sin15
y=30sin45-40sin15-25cos15
r^2=x^2+y^2
theta=arctan(y/x)

 

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The 105° comes from adding the 90° angle under the red vector in third picture with the
15° the blue vector is making, giving 105°.

The problem was asked to be solved in component form but I tried it this way & got
the wrong answer, I can't see why & am totally stumped & would just like to know
why.

 

[Mindscrape]

I don't know, round off errors most likely. Components are the way to go, less calculations.

 

[sponsoredwalk]

Yeah I had a good look at it & realized I'd assumed too much, I didn't calculate the
angle of the first resultant vector, I got a better answer, thanks!