Where Did I Go Wrong with the Cosine Formula?

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The discussion revolves around a misunderstanding of the cosine formula in triangle calculations. The user correctly set up the formula but mistakenly combined terms when calculating side 'a'. The error occurred when they multiplied the entire expression (58 - 42) by cos 35 instead of calculating 42 cos 35 first and then subtracting it from 58. The correct approach leads to the accurate answer of 4.86 cm for side 'a'. This highlights the importance of following the order of operations in mathematical calculations.
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I got this question wrong and I'm hoping someone can explain to me where I went wrong.

In a triangle...
angle A = 350
side b = 7 cm
side c = 3 cm

I need to find side a which is the side opposite angle A.

The formaula to use is -a2 = b2 + c2 - 2bc cos A
so, with the figures plugged in that comes out as...

a2 = 72 + 32 - 2 x 3 x 7 cos 35

which comes to...

a2 = 58 - 42 cos 35

SO FAR, I KNOW THAT IS CORRECT. I seem to have made the mistake at this point. I multiplied 16 (58-42) by cos 35 and took the square root of the answer, which gave me 3.62 cm.
However, apparently the right answer is 4.86 cm.
What did I do wrong?
 
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Gringo123 said:
I multiplied 16 (58-42) by cos 35 and took the square root of the answer, which gave me 3.62 cm.
However, apparently the right answer is 4.86 cm.
What did I do wrong?
58 - 42 cos 35 ≠ (58 - 42) cos35

58 - 42 cos 35 = 58 - (42 cos35)



Multiply 42 by cos35, then subtract that from 58.
 
That's brilliant! Thanks a lot Doc!
 

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