How do you determine whether $triangle ABC$ has no, one, or two solutions given $A=52^circ, a=9, b=20$ ?

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Answer 1 · 2018-06-21T07:16:14

$color(crimson)("As "sin B " can have a value only between " -1 " & "+1$ ,

$color(blue)("Given sum doesn't have a solution"$

![https://sites.google.com/site/trigingwithstarr/law-of-sines-and-cosines]( useruploads.socratic.org )

$hat A = 52^@, a = 9, b = 20$

Applying Law of Sines,

$a / sin A = b / sin B = c / sin C$

$sin B = (b sin A ) / a = (20 * sin 52 ) / 9 = 1.7511$

$"As "sin B " can have a value only between " -1 " & "+1$ ,

$"Given sum doesn't have a solution"$

How do you determine whether triangle ABCtriangle ABC has no, one, or two solutions given A=52^circ, a=9, b=20A=52^circ, a=9, b=20?