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# Cosine rule

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Hi good friends,

I am having trouble with finding an angle using the Cosine rule. The angle needed is A. The side opposite A measured 120. The other 2 sides are 100 each. I get an error when doing the calculation. The error reads: a+b>c.

Aug 31, 2022

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Law of cosines

The angle needed is A ($$\alpha$$)

Hello juriemagic,

you're talking about an isosceles triangle.

The other two sides together cannot be less than or equal to side c.

Then:

a = 120;  b = c = 100

$$Wanted: Angle\ \alpha$$

$$Law\ of\ cosines\\ a^2=b^2+c^2-2bccos\alpha\\ cos\alpha=\dfrac{b^2+c^2-a^2}{2bc}\\ cos\alpha=\dfrac{10^4+10^4-120^2}{2\cdot 10^4}\\ \alpha=arccos\ (\dfrac{10^4+10^4-120^2}{2\cdot 10^4})\\ \color{blue}\alpha =73.74^\circ$$ !

Aug 31, 2022
edited by asinus  Aug 31, 2022
#2
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Hello asinus,

I do appreciate your response and explanation. I'm not sure how I saw this, because I input the measurments in an app, and got an error message. AAAHHH, wait, something just occured to me now while typing here...OBVIOUSLY the long side cannot be greater or equal than the two shorter sides combined, because if it was at least equal, we would have two straight parrallel lines....NOT exceeding, in this case, 200. COMMON SENSE ....

Gosh, forgive my stupidity please, wasting your time on something like this. I do appreciate your time.

juriemagic  Sep 1, 2022