Find the value of a .

- briana.img

Find the value of a .

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- briana.img

I seriously just did a problem like this but I always forgot on how to use it

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- misty1212

HI!!

- misty1212

looks like a law of cosines problem?

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## More answers

- anonymous

sine law again.

- misty1212

hmm i think you need cosines for this
you do not know any angle opposite one of the known sides

- anonymous

right you are. Cosine law required.

- briana.img

\[\frac{ \sin52 }{ ? } = \frac{ sinb }{ 4 }\]

- 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

hold the phone dear

- 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

you do not have three out of any four, because you do not know the angle opposite any known side

- misty1212

you can see you ran in to that problem when you wrote
\[\frac{ \sin52 }{ ? } = \frac{ \sin(b) }{ 4 }\]

- 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

@misty1212 i got 5.52507014 from doing your way after square rooting

- misty1212

i can check if you like, i didn't do it

- briana.img

@misty1212 i think it's right but can you check it please

- misty1212

http://www.wolframalpha.com/input/?i=sqrt%284%5E2%2B7%5E2-2*4*7*cos%2852%29%29

- misty1212

5.52 rounded looks good

- briana.img

@misty1212 could you help me with another problem? please

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- misty1212

or in your case 5.5 cause they rounded to one decimal place

- 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

what do they want, \(r\) ?

- briana.img

@misty1212 trying to find the value of r which is reallyw eird

- misty1212

ok what is the measure of the angle opposite \(r\)?

- briana.img

@misty1212 there's no angle opposite of r that's the weird part

- misty1212

of course there is lol

- misty1212

it is labelled \(\huge R\)

- briana.img

@misty1212 there isn't!!

- misty1212

oh i see, you mean you don't know what it is

- misty1212

lets find it
total in the triangle is 180 so it is
\[180-45-63=72\]

- briana.img

@misty1212 oooh yeah lmao forgot you could do it like that

- misty1212

now law of sines finishes it right?

- misty1212

\[\frac{r}{\sin(72)}=\frac{22}{\sin(45)}\] etc

- briana.img

@misty1212 so it's rearrange to 22sin72=rsin45?

- misty1212

this time i notice they round to two places
http://www.wolframalpha.com/input/?i=22sin%2872%29%2Fsin%2845%29

- misty1212

that step is not necessary

- misty1212

\[\frac{r}{\sin(72)}=\frac{22}{\sin(45)}\iff r=22\times\frac{ \sin(72)}{\sin(45)}\]

- 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

@misty1212 r=29.58993453?

- misty1212

yeah looks good

- briana.img

@misty1212 thank you!!! you really helped me tonight htis lesson really got me messed up

- misty1212

you're welcome!\[\huge \color\magenta\heartsuit\]

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