Will someone correct my Trig homework?

[Gringo123]

I am currently studying Maths via the BBCBitesize website. The full address is:
http://www.bbc.co.uk/schools/gcsebitesize/maths/

I have just done the test at the end of the "further trigonometry - higher" section and I scored 8 / 15.

I don't understand where I went wrong on the 7 questions that I got wrong so I was wondering if anyone would be kind enough to take a look at my answers and give me some feedback?

 

[Mark44]

It would be better if you gave us the 7 questions and included your answers. I wasn't able to find anything in a quick scan of the link you provided.

 

[Gringo123]

Hi Mark
Firstly thanks for your offer of help.
I'll describe them 1 by 1 but as they all involve triangles and so on I guess you'll have to make a rough sketch yourself.
The first asks us to find the area of a triangle ABC.
angle CAB = 53 degrees
angle ABC = 105 degrees
angle BCA = 22 degrees
side AC is 7.1 cm

I know that in order to use the formula 0.5x a x b x SIN C I need to know the length of at least 2 sides and the angle between them. So first I work out the length of 1 of the unknown sides and I choose side a (BC).
so...
a/SIN A = b/ SIN B
which gives us...
a/ SIN 53 = 7.1/ SIN 105
so a = 7.1 / SIN B x SIN 53 = 5.87

so the length of side a (BC) is 5.87 c.m. I now have the length of 2 sides so I can use the formula 0.5 x a x b x SIN C
so... 0.5 x 5.87 x 7.1 x SIN C = 7.80 cm squared

But according to the website, this is the wrong answer. So is 7.79 which is what I get if I perform the calculations with the other unknown side AB.

Where am I going wrong?
Thanks again for your help

 

[Bohrok]

Here's the webpage with the problem, number 9
http://www.bbc.co.uk/apps/ifl/schools/gcsebitesize/maths/quizengine?quiz=furthertrigonometry&templateStyle=maths

 

[Bohrok]

I did it (using the other side of the triangle you didn't use) and my answer rounded to 7.81, which the site said was correct. Try not to round any of your numbers until the end.

 

[Gringo123]

I've got it now! But I have found that if work out the length of a side to say, 2.7535311
and then I shorten that to 2.75, that can make the difference between 1/100 of a unit. I only got the right answer when I starting using figures to 6 decimal places when giving the lengths of the 2 initially unknown sides.
Phew!
Anyway, many thanks to everyone for your help!

 

[Char. Limit]

There's a phrase I use: Never round until the end, if possible. If not, use every decimal you have.