Question 922882: side e= 52 side f=41 angle F=48
find all possible measures of angle E to the nearest degree
I know you must use the rules for an ambiguous cases. I have figured out all of the information I just need to know if it has one, two, or zero solutions. I believe it is one but I am not sure. I worked out that angle D is 61.52, angle E is 70.48, angle F is 48. I also know side e is 52, side f is 41, and side d is 48.49. Please tell me if it has 1,2, or 0 solutions. please & thank you!
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! side e= 52 side f=41 angle F=48
find all possible measures of angle E to the nearest degree
I know you must use the rules for an ambiguous cases. I have figured out all of the information I just need to know if it has one, two, or zero solutions. I believe it is one but I am not sure. I worked out that angle D is 61.52, angle E is 70.48, angle F is 48. I also know side e is 52, side f is 41, and side d is 48.49. Please tell me if it has 1,2, or 0 solutions. please & thank you!
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Using the Law of Sines, I get::
sin(E)/52 = sin(48)/41
sin(E) = 0.7431
E = arcsin(0.7431) = 48 or 180-48 = 132 degrees
But E cannot be 132 degrees because 48+48+132 > 180
Therefore E can only be 48 degrees
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Cheers,
Stan H.
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