- anonymous

Please help!

- katieb

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- anonymous

##### 1 Attachment

- jim_thompson5910

Start by drawing any generic triangle ABC
|dw:1434070079074:dw|

- jim_thompson5910

A = 43 degrees
B = 62 degrees
we can find C
A+B+C = 180
43+62+C = 180
C = 75
|dw:1434070139361:dw|

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## More answers

- jim_thompson5910

yes, BC = 22 and AB = unknown
Let x = AB
|dw:1434070198509:dw|

- anonymous

yes I know that much

- jim_thompson5910

now you use the law of sines
sin(A)/a = sin(C)/c
sin(43)/22 = sin(75)/x
solve for x

- anonymous

\[\frac{ \sin43 }{ 22 } = \frac{ \sin75 }{ x }\]

- anonymous

I'm honestly not sure how to solve for x @jim_thompson5910

- jim_thompson5910

using a calculator, you should find that
sin(75) = 0.96592582628907
sin(43) = 0.6819983600625

- jim_thompson5910

replace sin(43) and sin(75) with those approx values
cross multiply and then solve for x

- anonymous

ooh ok thank you

- anonymous

this is what I got...

##### 1 Attachment

- jim_thompson5910

you can also do it symbolically like this
\[\Large \frac{\sin(43)}{22}=\frac{\sin(75)}{x}\]
\[\Large \sin(43)*x=22*\sin(75)\]
\[\Large x=\frac{22*\sin(75)}{\sin(43)}\]
\[\Large x=???\]
treating sin(43) and sin(75) as if they are variables

- jim_thompson5910

desmos is in radian mode by default

- jim_thompson5910

click the wrench icon and switch to degree mode

- anonymous

Is there a place to put degrees in desmos?

- jim_thompson5910

it's off to the right side

- anonymous

oh thank you

- anonymous

so the first one is D?

- jim_thompson5910

yeah I get 31.1589725471071 which rounds to 31.2

- anonymous

Thanks I think I can get the 2nd on my own

- jim_thompson5910

np

- anonymous

|dw:1434070810160:dw|

- anonymous

|dw:1434070891025:dw|

- anonymous

sorry I'm just using this to walk myself through it you can leave @jim_thompson5910

- jim_thompson5910

alright, feel free to ask if you get stuck anywhere

- anonymous

great I'm already stuck -.-

- anonymous

I'm not sure what to use to find r... @jim_thompson5910

- jim_thompson5910

you need qr to find r (with the law of sines)
but before you can use the law of sines, you have to use the law of cosines to find qr

- anonymous

ok...

- jim_thompson5910

|dw:1434071160502:dw|

- anonymous

\[c^{2} = 7.5^{2} + 8.4^{2} - 2(7.5)(8.4)\cos(43)\]

- anonymous

like that?

- jim_thompson5910

very good

- jim_thompson5910

isolate c

- anonymous

ok I'm working it out now...

- anonymous

I got c = 7.54

- jim_thompson5910

me too

- anonymous

|dw:1434071506507:dw|

- jim_thompson5910

now you can use the law of sines

- anonymous

can you set it up for me like you did with the last one? I'm very bad at this...

- jim_thompson5910

the law of sines works like this
sin(A)/a = sin(B)/b = sin(C)/c
|dw:1434071589360:dw|

- jim_thompson5910

the letters pair up (upper and lower case)
A pairs with a
B with b
C with c
you'll have sin(A) pair with a, so that's how I got one fraction sin(A)/a
same with sin(B)/b
and sin(C)/c

- jim_thompson5910

normally you don't know the full picture of the triangle
so instead of saying sin(A)/a = sin(B)/b = sin(C)/c
you would use sin(A)/a = sin(B)/b
or sin(B)/b = sin(C)/c
or sin(A)/a = sin(C)/c

- anonymous

\[\frac{ \sin43 }{ 7.5 } = \frac{ \sin7.5 }{ x }\]

- anonymous

so this works?

- jim_thompson5910

I would use the full decimal expansion of qr instead of 7.5
or you can use a longer version, say qr = 7.5409365

- jim_thompson5910

and the second fraction won't have sin(7.5)

- jim_thompson5910

|dw:1434071876378:dw|

- jim_thompson5910

|dw:1434071921347:dw|

- anonymous

oh ok, so is this the right format (besides the larger decimal)?

- jim_thompson5910

do you see how I have sin(r)/7.5 ?

- anonymous

oooh ya I'll fix that

- anonymous

\[7.5= \frac{ 7.5*\sin x }{ \sin 43 }\]

- anonymous

I'm just screwing this up aren't I?

- jim_thompson5910

you're doing great

- jim_thompson5910

don't worry

- anonymous

ok but how do I isolate x?

- jim_thompson5910

First cross multiply. Then isolate sin(x). Finally use arcsine to fully isolate x
\[\Large \frac{\sin(43)}{7.5409365}=\frac{\sin(x)}{7.5}\]
\[\Large 7.5*\sin(43)=7.5409365*\sin(x)\]
\[\Large 7.5409365*\sin(x) = 7.5*\sin(43)\]
\[\Large \sin(x)=\frac{7.5*\sin(43)}{7.5409365}\]
\[\Large x=???\]

- anonymous

OOOH thank you so much!

- jim_thompson5910

what result do you get

- anonymous

um... I got lost after this far

##### 1 Attachment

- anonymous

I'm not sure what to do with the sin x to find x

- jim_thompson5910

the top 7.5 should use more decimal digits (say 4 or 5)

- jim_thompson5910

oops I meant the bottom 7.5

- anonymous

didn't change much

##### 1 Attachment

- jim_thompson5910

oh wait, I just realized that qr isn't 7.5
you were in radian mode on accident (I was too)

- jim_thompson5910

no wonder I'm not getting the answer choices

- anonymous

woooow XD ok then what is it??

- jim_thompson5910

this is the length of qr

##### 1 Attachment

- jim_thompson5910

QR = 5.887226 approximately
|dw:1434072742525:dw|

- anonymous

here's what I got

##### 1 Attachment

- jim_thompson5910

\[\Large \frac{\sin(43)}{5.887226}=\frac{\sin(x)}{7.5}\]
\[\Large 7.5*\sin(43)=5.887226*\sin(x)\]
\[\Large 5.887226*\sin(x) = 7.5*\sin(43)\]
\[\Large \sin(x)=\frac{7.5*\sin(43)}{5.887226}\]
\[\Large x=???\]

- anonymous

oh oops I changed the other 7.5 XD

- anonymous

there we go!

##### 1 Attachment

- jim_thompson5910

now evaluate the arcsine of that number

- jim_thompson5910

##### 1 Attachment

- anonymous

Ta Da!

##### 1 Attachment

- jim_thompson5910

you nailed it

- anonymous

so its D?

- jim_thompson5910

both seem to be D, yes
I guess the makers weren't too creative

- anonymous

haha well thank you SO much! *hugs*

- jim_thompson5910

you're welcome

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