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I was given a triangle:

side opposite of angle A: unknown, referred to as L

side adjacent of angle A: 11'

hypotenuse: 14'

I have to find the cosine of angle A, the degrees, and the length of "L", opposite angle A, in feet.

L is equal to 8.6602, which in feet is 8'-7 7/16. I did the math, and got angle A= 38 degrees

(my instructor wants length in feet-inches-fraction, I'm in pipefitters school. He also doesn't want minutes or seconds for the angles)

However, when I did the cosine function, I ended up with .999905 We are supposed to round decimals to the fourth place. However, that leaves me with

.9999

which should round up to

1

But...what I'm wondering is can I even have a whole number for a cosine, or should I leave it at .9999?

If .9999 is the mathematically correct answer, I need to know why, in order to defend it in class. If 1 is the correct answer, then I'd just like to know why. However, I asked Google and haven't been able to get an answer that I understand.

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    The cosine of 0 degrees is 1. To see this, draw a right angle "triangle" of side lengths 0, 1, 1...2012-03-10
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    The cosine function of what? There is nothing in the picture that has cosine equal to $0.999905$. The cosine of an angle in a triangle cannot be $1$. Cosines near $1$ are for angles fairly close to $0$.2012-03-10
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    If you have a right angled triangle with: angle A, side length opposite A is L, side length adjacent to A is 11 and hypotenuse is 14, then I would say that $\cos(A) = 11 / 14= 0.7857...$. And so the angle $A$ is $\cos^{-1}(0.7857) = 48.17$ degrees. I don't understand where your 0.9999 comes from...2012-03-10
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    Oh, and if you round $0.999905$ to the forth place then you get $0.9999$ which isn't equal to $1$.2012-03-10
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    Well your L is correct and $\displaystyle \arccos\left(\frac{11}{14}\right)\approx 0.789774$ is indeed approximatively $38.21$ degrees but it seems to me that the $\cos$ should be $\frac{11}{14}=\cos(0.789774...)$ no? Where did you evaluate the $\cos$ function?2012-03-10
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    for cos I did cos(11/14) and my calculator gave me .999905 The way I reached 1 is if I write it as .9999 (as we are told to do, to the fourth decimal), our instructor has told us to round up to 1. (this also applies to .9875, anything that can be rounded up to a whole number)2012-03-11
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    Ok so you computed $\cos(\frac{11}{14}°)$ but the cosine is just : adjacent side/hypotenuse = $\frac{11}{14}$ (further $\frac{11'}{14'}$ can't be in degrees). Your instructor wanted you to find the cosine $=\frac{11}{14}$, the corresponding degrees $\arccos(\frac{11}{14})\approx 38.21$ and the length $L=\sqrt{14^2-11^2}$ you were wrong only for the first part. Hoping this and Michael's answer helped,2012-03-11
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    oh! That makes sense now! Thank you so much!2012-03-11
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    Since I up-voted this question and it's total is $0$, someone must have down-voted it, showing again the inefficacy of that as a communications medium, since there's no way to know why.2012-03-12

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