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How do I find the cosine of this angle?

I’m taking a practice math test and I’m confused.. The problem says: In a triangle ABC, AB=7, AC=8, and BC=3. What is cos(A)? So I used the cosine=adjacent/hypotenuse formula and got 7/8 as the answer, which is one of the four choices, however when I checked it it says the right answer is 13/14, and to use the Law of Cosine. I looked that up because I didn’t know what it was and it says c^2=a^2+b^2-2abCos(C). I tried solving the problem with that formula and didn’t get 13/14. So basically, what am I doing wrong and why is the way I tried to solve it incorrect? Thanks.

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Answer #1

AB is your c. AC is your b. BC is your a. a^2=b^2+c^2-2bcCos(A) which is just a variation of your c^2=a^2+b^2-2abCos(C) formula because you are solving for A instead of C.

3^2=8^2+7^2-2(8)(7)Cos(A) 9=64+49-112Cos(A) 112CosA=104 CosA=104/112 Simplify that and viola 13/14

You were simply using the wrong angles and wrong variation of the formula.

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