Trigonometry - I think it is cosine rule

[elly39951]

Hi All - I joined further maths recently and do not get how to do this question

In triangle ABC, a=8, c=12 and C=52 degrees

(a) Draw and label the triangle (you don't have to do this)

and
 
(b) Now find angle A correct to 1 decimal place.

The rule is not making sense with to me with the information given! Please Help.

[Stick]

You need to draw the triangle. Don't ever attempt these questions without a diagram! I'll explain what you can do to determine whether you need to use the sine or cosine rule, but it requires a sketch.

If a side length has a defined angle on the opposite vertex (it doesn't matter if the angle/side length is an actual number or an unknown variable), draw a loop around the two. If you get two loops, use the sine rule. If you get just one, use the cosine rule. I personally called these "propellers" and "arrowheads" to remember, but that's not really crucial.

Good luck.

[elly39951]

Thanks, it makes sense now!!
But I thought I had to use the cosine rule because I am given two side lengths and an included angle. So I don't understand why I have to use the sine rule?? Or is the angle given non-included?- What do these mean?

[Homer]

for cosine rule the angle must be of the unknow side length



therefore if you were to use the cosine rule you would get



which you wouldn't be able to solve since you are not given the value of b

[Daenerys Targaryen]

I use Cosine when I have information on all three, may A and b and c and asking for a

And Sine Rule when I have 1 info on one thing and 2 on another such as A and C and c, or b, c, B.
Remembering with Sine Rule if you dont have an included angle you may have the ambiguous case of the sine rule, where you minus the angle found by 180.