Question

Find the exact value of tan θ.

Answer 1

Answer:

The answer is C.

Step-by-step explanation:

Recall SohCahToa, where $tan(\theta)=opp/adj$.

In the triangle, the opposite (to angle theta) is $6$, while the adjacent is $2\sqrt{5}$.

Put this into the equation:

$tan(\theta)=\frac{6}{2\sqrt5}$

Now, simplify: (multiply both top and bottom by $\sqrt5$

$\frac{6}{2\sqrt{5} } \cdot\frac{\sqrt{5} }{\sqrt{5}} =\frac{6\sqrt{5}}{2(5)} =\frac{6\sqrt{5}}{10}=\frac{3\sqrt{5} }{5}$

The answer is C.