given △qrs ~ △xyz, what is the value of tan(q)?\no $\frac{3}{5}$\no $\frac{3}{4}$\no $\frac{4}{5}$\no…

Explanation:

Step1: Recall tangent ratio and similarity property

For right - angled triangles, $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$. Since $\triangle QRS\sim\triangle XYZ$, corresponding angles are equal, so $\angle Q=\angle X$.

Step2: Identify opposite and adjacent sides for $\angle X$

In right - angled $\triangle XYZ$, for $\angle X$, the opposite side to $\angle X$ is $YZ = 9$ and the adjacent side is $XZ=12$.

Step3: Calculate $\tan(X)$

$\tan(X)=\frac{YZ}{XZ}=\frac{9}{12}=\frac{3}{4}$. Since $\angle Q=\angle X$, $\tan(Q)=\frac{3}{4}$.

Answer:

$\frac{3}{4}$