Find the value of each trigonometric ratio.
5) $\sin Z$
A) $\frac{12}{5}$
B) $\frac{5}{13}$
C) $\frac{13}{12}$
D) $\frac{5}{12}$

Answer

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Answer

\boxed{\frac{12}{13}}

Steps

Step 1 ：$\sin^2 Z + \cos^2 Z = 1$

Step 2 ：$\sin^2 Z = 1 - \cos^2 Z$

Step 3 ：$\sin^2 Z = 1 - \left(\frac{5}{13}\right)^2$

Step 4 ：$\sin^2 Z = 1 - \frac{25}{169}$

Step 5 ：$\sin^2 Z = \frac{144}{169}$

Step 6 ：$\sin Z = \pm\frac{12}{13}$

Step 7 ：\boxed{\frac{12}{13}}