Question

given △abc - △xyz, what is the value of cos(z)?

Explanation:

Step1: Recall cosine ratio and similarity property

For right - angled triangles, $\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}$. Since $\triangle ABC\sim\triangle XYZ$, corresponding angles are equal. $\angle C=\angle Z$.

Step2: Identify adjacent and hypotenuse for $\angle C$ in $\triangle ABC$

In right - angled $\triangle ABC$ with right - angle at $B$, for $\angle C$, the adjacent side to $\angle C$ is $BC = 12$ and the hypotenuse is $AC=13$.

Step3: Calculate $\cos(Z)$

Since $\angle C=\angle Z$, $\cos(Z)=\cos(C)=\frac{BC}{AC}=\frac{12}{13}$.

Answer:

$\frac{12}{13}$