Find the value of a .

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Find the value of a .

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I seriously just did a problem like this but I always forgot on how to use it
HI!!
looks like a law of cosines problem?

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Other answers:

sine law again.
hmm i think you need cosines for this you do not know any angle opposite one of the known sides
right you are. Cosine law required.
\[\frac{ \sin52 }{ ? } = \frac{ sinb }{ 4 }\]
\[a^2=b^2+c^2-2bc\cos(A)\] \[a^2=4^2+7^2-2\times 4\times \cos(52^\circ)\] and a calcullator
hold the phone dear
if you want to use the law of sines (which you do , because it is easiest) you need 3 out of the for numbers to make a ratio
you do not have three out of any four, because you do not know the angle opposite any known side
you can see you ran in to that problem when you wrote \[\frac{ \sin52 }{ ? } = \frac{ \sin(b) }{ 4 }\]
you got only two of the four numbers, two are unknown so you must use the law of cosines for this one
@misty1212 i got 5.52507014 from doing your way after square rooting
i can check if you like, i didn't do it
@misty1212 i think it's right but can you check it please
http://www.wolframalpha.com/input/?i=sqrt%284%5E2%2B7%5E2-2*4*7*cos%2852%29%29
5.52 rounded looks good
@misty1212 could you help me with another problem? please
or in your case 5.5 cause they rounded to one decimal place
yeah but i can't read what they are trying to find the value of in this case you know two angles so you know all three and therefore you can use the law of sines
what do they want, \(r\) ?
@misty1212 trying to find the value of r which is reallyw eird
ok what is the measure of the angle opposite \(r\)?
@misty1212 there's no angle opposite of r that's the weird part
of course there is lol
it is labelled \(\huge R\)
@misty1212 there isn't!!
oh i see, you mean you don't know what it is
lets find it total in the triangle is 180 so it is \[180-45-63=72\]
@misty1212 oooh yeah lmao forgot you could do it like that
now law of sines finishes it right?
\[\frac{r}{\sin(72)}=\frac{22}{\sin(45)}\] etc
@misty1212 so it's rearrange to 22sin72=rsin45?
this time i notice they round to two places http://www.wolframalpha.com/input/?i=22sin%2872%29%2Fsin%2845%29
that step is not necessary
\[\frac{r}{\sin(72)}=\frac{22}{\sin(45)}\iff r=22\times\frac{ \sin(72)}{\sin(45)}\]
i know some math teacher might have said "cross multiply" but they are silly \[\frac{x}{a}=\frac{b}{c}\iff x=\frac{ab}{c}\]
@misty1212 r=29.58993453?
yeah looks good
@misty1212 thank you!!! you really helped me tonight htis lesson really got me messed up
you're welcome!\[\huge \color\magenta\heartsuit\]

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