Answer:
One triangle
Step-by-step explanation:
step 1
Find the measure of side AC
In the right triangle of the left
[tex]sin(33^o)=\frac{9}{AC}[/tex] ----> by SOH (opposite side divided by the hypotenuse)
[tex]AC=\frac{9}{sin(33^o)}=16.5\ in[/tex]
step 2
Find the measure of angle B
Applying the law of sines
[tex]\frac{a}{Sin(A)}=\frac{b}{Sin(B)}[/tex]
substitute the given values
[tex]\frac{15}{Sin(33^o)}=\frac{16.5}{Sin(B)}[/tex]
[tex]Sin(B)=\frac{16.5}{15}Sin(33^o)=0.60[/tex]
[tex]B=sin^{-1}(0.60)= 36.87^o[/tex]
step 3
Find the measure of angle C
Remember that the sum of the interior angles of a triangle must be equal to 180 degrees
so
[tex]33^o+36.87^o+ C=180^o[/tex]
[tex]C=110.13^o[/tex]
step 4
Find the measure of side AB
Applying the law of sines
[tex]\frac{a}{Sin(A)}=\frac{c}{Sin(C)}[/tex]
substitute the given values
[tex]\frac{15}{Sin(33^o)}=\frac{c}{Sin(110.13^o)}[/tex]
[tex]c=15\frac{Sin(110.13^o)}{Sin(33^o)}=25.9\ m[/tex]
Each measure of the ABC triangle can only have one value, therefore only one triangle can be make with the given measures
