Question

given △abc ~ △xyz, what is the value of cos(z)?
options:

• $\frac{5}{13}$
• $\frac{5}{12}$
• $\frac{12}{13}$
• $\frac{12}{5}$

Explanation:

Step1: Identify correspondence

ΔABC ~ ΔXYZ implies ∠C=∠Z.

Step2: Right triangle ABC

∠B=90°, sides: AB=5, BC=12, AC=13 (hypotenuse).

Step3: Calculate cos(C)

cos(C)=adjacent/hypotenuse=BC/AC=12/13.

Step4: cos(Z)=cos(C)

Thus, cos(Z)=12/13.

Answer:

C. 12/13