Answer:
[tex]\huge\boxed{B.\ \dfrac{12}{35}}[/tex]
Step-by-step explanation:
Look at the picture.
We know:
[tex]\sin\theta=\dfrac{a}{c}\\\\\tan\theta=\dfrac{a}{b}[/tex]
We have
[tex]\sin\theta=\dfrac{12}{37}\Rightarrow a=12,\ c=37[/tex]
Use the Pythagorean theorem.
[tex]a^2+b^2=c^2\\\\12^2+b^2=37^2\\\\144+b^2=1369\qquad|\text{subtract 144 from both sides}\\\\b^2=1225\to b=\sqrt{1225}\\\\b=35[/tex]
Calculate tangent:
[tex]\tan\theta=\dfrac{12}{35}[/tex]
