Answer:
c. One
Step-by-step explanation:
step 1
Find the value of B
Applying the law of sines
[tex]\frac{a}{Sin(A)}=\frac{b}{Sin(B)}[/tex]
substitute the given values
[tex]\frac{23}{Sin(61^o)}=\frac{24}{Sin(B)}[/tex]
[tex]Sin(B)=\frac{24}{23}Sin(61^o)[/tex]
[tex]B=Sin^{-1}(\frac{24}{23}Sin(61^o))=65.87^o[/tex]
step 2
Find the measure of angle C
Remember that the sum of the interior angles in any triangle must be equal to 180 degrees
so
[tex]61^o+65.87^o+C=180^o[/tex]
[tex]C=53.13^o[/tex]
step 3
Find the value of c
Applying the law of sines
[tex]\frac{a}{Sin(A)}=\frac{c}{Sin(C)}[/tex]
substitute the given values
[tex]\frac{23}{Sin(61^o)}=\frac{c}{Sin(53.13)}[/tex]
[tex]c=\frac{23}{Sin(61^o)}Sin(53.13)[/tex]
[tex]c=21.04\ units[/tex]
so
there can only be one value for each measurement, therefore there can only be one triangle
