Law of Sines- The Ambiguous Case 1) m

Mathematics
- anonymous

Law of Sines- The Ambiguous Case 1) m

Mathematics
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- anonymous

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## More answers

- anonymous

lets 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

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- anonymous

sorry for the lousy picture, but you can see you have two choices for angle A

- anonymous

in big triangle angle A is 180-29-33.82 = 117.18

- anonymous

That 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

these are not right triangles so you do not have "opposite" and "adjacent"

- anonymous

i 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

My teacher gave us notes and it says if you have two sides & one opposite (NON-included) angle of a triangle then there are three possibilities:

- anonymous

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- anonymous

How is this determined? opp \[\ge\] adj or opp \[\le\] adj

- anonymous

that is the larger triangle, and first we solve for B because you have angle C, side c, and side b

- anonymous

so 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

i labled them with the side c opposite angle C, side a opposite angle A and side b opposite angle B

- anonymous

then you can use
\[\frac{\sin(A)}{a}=\frac{\sin(B)}{b}=\frac{\sin(C)}{c}\][

- anonymous

and 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

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