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

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}}