Question

in the figure below, △abc ~ △zxy. find sin z, tan z, and cos z. round your answers to the nearest hundredth.

Explanation:

Step1: Use similarity of triangles

Since $\triangle ABC\sim\triangle ZXY$, corresponding - angle ratios are equal. $\angle Z$ corresponds to $\angle A$. In right - triangle $ABC$, $\sin A=\frac{BC}{AB}$, $\tan A = \frac{BC}{AC}$, $\cos A=\frac{AC}{AB}$.

Step2: Calculate $\sin Z$

$\sin Z=\sin A=\frac{BC}{AB}=\frac{9.6}{29.6}\approx0.32$

Step3: Calculate $\tan Z$

$\tan Z=\tan A=\frac{BC}{AC}=\frac{9.6}{28}\approx0.34$

Step4: Calculate $\cos Z$

$\cos Z=\cos A=\frac{AC}{AB}=\frac{28}{29.6}\approx0.95$

Answer:

$\sin Z\approx0.32$, $\tan Z\approx0.34$, $\cos Z\approx0.95$