briana.img
  • briana.img
Find the value of a .
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
briana.img
  • briana.img
I seriously just did a problem like this but I always forgot on how to use it
misty1212
  • misty1212
HI!!
misty1212
  • misty1212
looks like a law of cosines problem?

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More answers

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

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