Answer: 1
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Step-by-step explanation
Let's use the law of sines to determine angle "A".
sin(A)/a = sin(C)/c
sin(A)/16.3 = sin(39.3)/24.1
sin(A) = 16.3*sin(39.3)/24.1
sin(A) = 0.428386 approximately
A = arcsin(0.428386) or A = 180-arcsin(0.428386)
A = 25.365175 or A = 154.634825
Both results are approximate.
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If A = 25.365175, then,
A+B+C = 180
B = 180-A-C
B = 180-25.365175-39.3
B = 115.334825
This result is in the interval 0 < B < 180, so we have a valid triangle here.
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If A = 154.634825, then,
A+B+C = 180
B = 180-A-C
B = 180-154.634825-39.3
B = -13.934825
This result is NOT in the interval 0 < B < 180, so a triangle cannot be formed when A = 154.634825 degrees.
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To summarize, a triangle is only possible when angle A = 25.365175 degrees approximately.
Therefore, only one triangle is possible.
A tool like GeoGebra can be used to confirm the answer.