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anonymous
 4 years ago
Law of Sines The Ambiguous Case 1) m<C=29 degrees b=31 m c=27 m
anonymous
 4 years ago
Law of Sines The Ambiguous Case 1) m<C=29 degrees b=31 m c=27 m

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anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0dw:1328495762650:dw

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0I don't get how to start. :/

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0lets find the big triangle first. by the law of sines you have \[\frac{\sin(29)}{27}=\frac{\sin(B)}{31}\] \[\frac{31\sin(29)}{27}=\sin(B)\] \[\sin(B)=.5566\] rounded so \[B=\sin^{1}(.5566)=33.82\]

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0dw:1328496308131:dw

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0sorry for the lousy picture, but you can see you have two choices for angle A

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0in big triangle angle A is 1802933.82 = 117.18

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0That first response was great definitely helped! But what number would be the opposite & what number would be the adj? Cause that will help me determine the # of triangles.

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0these are not right triangles so you do not have "opposite" and "adjacent"

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0i was looking at the largter triangle first and using the laws of sines, because the invese sine funcion on your calculator will not give you the bigger angle, only the one less that 90 degrees

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0My teacher gave us notes and it says if you have two sides & one opposite (NONincluded) angle of a triangle then there are three possibilities:

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0dw:1328496610821:dw

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0How is this determined? opp \[\ge\] adj or opp \[\le\] adj

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0that is the larger triangle, and first we solve for B because you have angle C, side c, and side b

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0so you know three out of the 4 numbers for the ratio it is not a matter of "opposite" "adjacent" etc because these are not right triangles

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0i labled them with the side c opposite angle C, side a opposite angle A and side b opposite angle B

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0then you can use \[\frac{\sin(A)}{a}=\frac{\sin(B)}{b}=\frac{\sin(C)}{c}\][

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0and since we know side c, angle C, side b we have three out of the 4 numbers for the ratio here \[\frac{\sin(B)}{b}=\frac{\sin(C)}{c}\] allowing us to solve for angle B

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0So the answer to find m<A is 117 degrees?

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0the reason this is the "ambiguous case" is that there are two possible triangles, the ones i drew in the first picture. in the bigger triangle and A is 117.18

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0*has angle A = 117.18

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0the smaller triangle has a different angle, but that is now easy to find

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0dw:1328497019018:dw

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0Thank you so much! I got the hang of this now :)

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0the other angle B, the one in the smaller triangle, has measure 180  33.82 = 146.18

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0so the measure of angle A in the smaller triangle is \[180  29  146.18 = 4.82\]
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