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# C2 Triangles problem Watch

1. The perimeter of triangle ABC is 15cm
Given that AB = 7cm and angle BAC is 60 degrees, find the lengths of AC and BC.

I dont know what to do as Ive only got one angle and one side. Ive tried splitting it into two 90 triangles but this didnt help much. I dont think i know how to make use of the fact that the perimeter is 15cm....
2. If someone would correct me if there's an easier way of doing this, but you it seems to me that the cosine rule is the way to go. Firstly I'd label the sides a, b and c (opposite to the angles A, B and C respectively). You should be able to form two equations with the information you've been given - one is of course that a+b+c=15 and as c=7, a+b=8.

Form an equation with the cosine rule, then look at solving them simultaneously.
3. (Original post by mb100)
If someone would correct me if there's an easier way of doing this, but you it seems to me that the cosine rule is the way to go. Firstly I'd label the sides a, b and c (opposite to the angles A, B and C respectively). You should be able to form two equations with the information you've been given - one is of course that a+b+c=15 and as c=7, a+b=8.

Form an equation with the cosine rule, then look at solving them simultaneously.
Well, I got

a^2 - b^2 - c^2 = bc from the cosine rule

a+b + c = 15 from the perimeter

But i don't think I can solve these seeing as there are three variables....
4. Cosine rule is a^2=b^2+c^2- 2bccosA, you've already put cosA in to get a^2=b^2+c^2-bc, but then a minus went missing from the bc. So really it should be a^2 - b^2 - c^2 = -bc

But remember you already have one of the variables from the side that you've been given, as line AB = 7cm, if you refer to your diagram (or just picture it in your head) it would be opposite angle C, so c=7. Substitute 7 for c and solve for a and b.
5. and then solve simultaneously a+b = 8 with 8a-49 = b

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