Where Did I Go Wrong with the Cosine Formula?

[Gringo123]

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?

 

[Doc Al]

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.

 

[Gringo123]

That's brilliant! Thanks a lot Doc!