Answer:
The answer is C.
Step-by-step explanation:
Recall SohCahToa, where
[tex]\displaystyle \tan(\theta)=\frac{\text{opposite}}{\text{adjacent}}[/tex].
In the triangle, the opposite (to angle θ) is [tex]6[/tex], while the adjacent is [tex]2\sqrt{5}[/tex].
By substitution:
[tex]\displaystyle \tan(\theta)=\frac{6}{2\sqrt5}[/tex]
Simplify:
[tex]\displaystyle \frac{6}{2\sqrt{5} } \cdot\frac{\sqrt{5} }{\sqrt{5}} =\frac{6\sqrt{5}}{2(5)} =\frac{6\sqrt{5}}{10}=\frac{3\sqrt{5} }{5}[/tex]
The answer is C.
