In what cases will there be two answers when finding the angles and sides using the Law of Sines? TEST IN HOUR?

For example, A= 11 degrees, b=7, and a =5





For some reason there are two answers. I do not understand why.





Please help I have a test in about 1 hour!!In what cases will there be two answers when finding the angles and sides using the Law of Sines? TEST IN HOUR?
a / sinA = b / sinB


5 / sin11潞 = 7 / sinB


26.204 = 7/sinB


sinB = 0.267


B = about 15.486潞





B can also equal about 164.486潞





sin(x) is periodic, meaning it goes up and goes down and back up, etc etc....


so you can have 2 angles whose sin's are the same








and since you do not know your 3rd side or angle, you cannot figure out if B is an acute or obtuse angle...In what cases will there be two answers when finding the angles and sides using the Law of Sines? TEST IN HOUR?
I'm assuming the 11 degrees are opposite the side that is 5 units?





Then, sin11/5 as sin@/7 To get the third angle, you then subtract @+11 from 180; then, once you have that angle, say, it's angle THETA, sinTHETA/c as sin11/5 to find the third side.
Probably when the angle is not opposite the longest side (or perhaps the longer of the two given sides, or the angle is not the included angle, like here).





I need to explore this one!
if the angle is %26lt; 90 degrees, then there are 2 possibilities since sin x = sin(180 - x).
'A' is the angle opposite of side 'a', 'b' is an adjacent side.


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