anonymous
  • anonymous
In triangle ABC , m angle A=41 degrees, m angle B=32 degrees and AC= 9 inches what is AB to the nearest tenth of an inch a. 13.1 in b. 13.6 in c. 16.2 in d. 16.9 in
Mathematics
  • Stacey Warren - Expert brainly.com
Hey! We 've verified this expert answer for you, click below to unlock the details :)
SOLVED
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
jamiebookeater
  • jamiebookeater
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
anonymous
  • anonymous
|dw:1432846650149:dw| I'm assuming it looks like this?
anonymous
  • anonymous
i guess? it didnt have a picture on this one
johnweldon1993
  • johnweldon1993
So this can just be solved with the law of sines You have your triangle *drawn above* and you have the length of 1 other side So we can use \[\large \frac{sin(32)}{9} = \frac{sin(107)}{AB}\] And solve for AB

Looking for something else?

Not the answer you are looking for? Search for more explanations.

More answers

anonymous
  • anonymous
ok and i solve for AB how? @johnweldon1993
johnweldon1993
  • johnweldon1993
Wait, first, have you seen this before? The law of sines?
anonymous
  • anonymous
can you walk me through this? or would that be asking for to much? @johnweldon1993 and no i changed schools and skiped like 3 units so im trying to get all of this
johnweldon1993
  • johnweldon1993
No never asking too much :) but first, what class is the for? I just dont want to introduce something you wouldnt even be learning :)
anonymous
  • anonymous
Algebra 2
johnweldon1993
  • johnweldon1993
Okay then yeah this applies :) Okay so...in general You have a triangle |dw:1432852105182:dw|
johnweldon1993
  • johnweldon1993
So first we need to solve for angle C We know that the interior angles of a triangle always add to 180 So since we have 41...and 32...we have 73 of those 180 degrees So angle C must be the remaining 107 degrees right?
anonymous
  • anonymous
ok...
johnweldon1993
  • johnweldon1993
does that make sense? Gotta make sure you're staying with me :)
anonymous
  • anonymous
yes im with you
johnweldon1993
  • johnweldon1993
So now, we apply the law of sines What THAT states...is: \[\large \frac{sin(A)}{a} = \frac{sin(B)}{b} = \frac{sin(C)}{c}\] Where A,B and C are the angle measurements we have and a,b and c are the side lengths we have
johnweldon1993
  • johnweldon1993
Now the way we use it....is if we have angle A, then side "A" would be the side the angle faces |dw:1432852557818:dw|
anonymous
  • anonymous
that's familiar
johnweldon1993
  • johnweldon1993
So...since you have side B right...here it would be AC |dw:1432852698148:dw| And you want to solve for side C which here would be AB |dw:1432852734405:dw| we can write \[\large \frac{sin(\text{Angle of B)}}{\text{Length of side B = 9}} = \frac{sin(\text{angle of C)}}{\text{length of side C = ???}}\] \[\large \frac{sin(32)}{9} = \frac{sin(107)}{AB}\]
johnweldon1993
  • johnweldon1993
And then we just solve for AB Now to do that...we just cross multiply \[\large ABsin(32) = 9sin(107)\] And divide both sides by the sin(32) so \[\large AB = \frac{9sin(107)}{sin(32)}\]
anonymous
  • anonymous
ok.. um sorry its taking a while for me to catch on
johnweldon1993
  • johnweldon1993
No that's fine :) just tell me if you want me to explain a part over :)
anonymous
  • anonymous
it was pretty explanatory just takes a lot of practice thank you so much!
johnweldon1993
  • johnweldon1993
Of course :)

Looking for something else?

Not the answer you are looking for? Search for more explanations.