anonymous
  • anonymous
Please help!
Mathematics
katieb
  • katieb
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
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anonymous
  • anonymous
1 Attachment
jim_thompson5910
  • jim_thompson5910
Start by drawing any generic triangle ABC |dw:1434070079074:dw|
jim_thompson5910
  • 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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jim_thompson5910
  • jim_thompson5910
yes, BC = 22 and AB = unknown Let x = AB |dw:1434070198509:dw|
anonymous
  • anonymous
yes I know that much
jim_thompson5910
  • 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
  • anonymous
\[\frac{ \sin43 }{ 22 } = \frac{ \sin75 }{ x }\]
anonymous
  • anonymous
I'm honestly not sure how to solve for x @jim_thompson5910
jim_thompson5910
  • jim_thompson5910
using a calculator, you should find that sin(75) = 0.96592582628907 sin(43) = 0.6819983600625
jim_thompson5910
  • jim_thompson5910
replace sin(43) and sin(75) with those approx values cross multiply and then solve for x
anonymous
  • anonymous
ooh ok thank you
anonymous
  • anonymous
this is what I got...
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jim_thompson5910
  • 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
  • jim_thompson5910
desmos is in radian mode by default
jim_thompson5910
  • jim_thompson5910
click the wrench icon and switch to degree mode
anonymous
  • anonymous
Is there a place to put degrees in desmos?
jim_thompson5910
  • jim_thompson5910
it's off to the right side
anonymous
  • anonymous
oh thank you
anonymous
  • anonymous
so the first one is D?
jim_thompson5910
  • jim_thompson5910
yeah I get 31.1589725471071 which rounds to 31.2
anonymous
  • anonymous
Thanks I think I can get the 2nd on my own
jim_thompson5910
  • jim_thompson5910
np
anonymous
  • anonymous
|dw:1434070810160:dw|
anonymous
  • anonymous
|dw:1434070891025:dw|
anonymous
  • anonymous
sorry I'm just using this to walk myself through it you can leave @jim_thompson5910
jim_thompson5910
  • jim_thompson5910
alright, feel free to ask if you get stuck anywhere
anonymous
  • anonymous
great I'm already stuck -.-
anonymous
  • anonymous
I'm not sure what to use to find r... @jim_thompson5910
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
  • anonymous
ok...
jim_thompson5910
  • jim_thompson5910
|dw:1434071160502:dw|
anonymous
  • anonymous
\[c^{2} = 7.5^{2} + 8.4^{2} - 2(7.5)(8.4)\cos(43)\]
anonymous
  • anonymous
like that?
jim_thompson5910
  • jim_thompson5910
very good
jim_thompson5910
  • jim_thompson5910
isolate c
anonymous
  • anonymous
ok I'm working it out now...
anonymous
  • anonymous
I got c = 7.54
jim_thompson5910
  • jim_thompson5910
me too
anonymous
  • anonymous
|dw:1434071506507:dw|
jim_thompson5910
  • jim_thompson5910
now you can use the law of sines
anonymous
  • anonymous
can you set it up for me like you did with the last one? I'm very bad at this...
jim_thompson5910
  • jim_thompson5910
the law of sines works like this sin(A)/a = sin(B)/b = sin(C)/c |dw:1434071589360:dw|
jim_thompson5910
  • 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
  • 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
  • anonymous
\[\frac{ \sin43 }{ 7.5 } = \frac{ \sin7.5 }{ x }\]
anonymous
  • anonymous
so this works?
jim_thompson5910
  • 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
  • jim_thompson5910
and the second fraction won't have sin(7.5)
jim_thompson5910
  • jim_thompson5910
|dw:1434071876378:dw|
jim_thompson5910
  • jim_thompson5910
|dw:1434071921347:dw|
anonymous
  • anonymous
oh ok, so is this the right format (besides the larger decimal)?
jim_thompson5910
  • jim_thompson5910
do you see how I have sin(r)/7.5 ?
anonymous
  • anonymous
oooh ya I'll fix that
anonymous
  • anonymous
\[7.5= \frac{ 7.5*\sin x }{ \sin 43 }\]
anonymous
  • anonymous
I'm just screwing this up aren't I?
jim_thompson5910
  • jim_thompson5910
you're doing great
jim_thompson5910
  • jim_thompson5910
don't worry
anonymous
  • anonymous
ok but how do I isolate x?
jim_thompson5910
  • 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
  • anonymous
OOOH thank you so much!
jim_thompson5910
  • jim_thompson5910
what result do you get
anonymous
  • anonymous
um... I got lost after this far
1 Attachment
anonymous
  • anonymous
I'm not sure what to do with the sin x to find x
jim_thompson5910
  • jim_thompson5910
the top 7.5 should use more decimal digits (say 4 or 5)
jim_thompson5910
  • jim_thompson5910
oops I meant the bottom 7.5
anonymous
  • anonymous
didn't change much
1 Attachment
jim_thompson5910
  • 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
  • jim_thompson5910
no wonder I'm not getting the answer choices
anonymous
  • anonymous
woooow XD ok then what is it??
jim_thompson5910
  • jim_thompson5910
this is the length of qr
jim_thompson5910
  • jim_thompson5910
QR = 5.887226 approximately |dw:1434072742525:dw|
anonymous
  • anonymous
here's what I got
1 Attachment
jim_thompson5910
  • 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
  • anonymous
oh oops I changed the other 7.5 XD
anonymous
  • anonymous
there we go!
1 Attachment
jim_thompson5910
  • jim_thompson5910
now evaluate the arcsine of that number
jim_thompson5910
  • jim_thompson5910
anonymous
  • anonymous
Ta Da!
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jim_thompson5910
  • jim_thompson5910
you nailed it
anonymous
  • anonymous
so its D?
jim_thompson5910
  • jim_thompson5910
both seem to be D, yes I guess the makers weren't too creative
anonymous
  • anonymous
haha well thank you SO much! *hugs*
jim_thompson5910
  • jim_thompson5910
you're welcome

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