Answer
$sin~\theta=\frac{opp}{hyp}=\frac{8}{17}$
$tan~\theta=\frac{opp}{adj}=\frac{8}{15}$
$cot~\theta=\frac{adj}{opp}=\frac{15}{8}$
$sec~\theta=\frac{hyp}{adj}=\frac{17}{15}$
$csc~\theta=\frac{hyp}{opp}=\frac{17}{8}$
Work Step by Step
$cos~\theta=\frac{adj}{hyp}$
$\frac{15}{17}=\frac{adj}{hyp}$
A right triangle with a hypotenuse equal to $17$ and with the adjacent side of $\theta$ equals $15$ has a cosine equal to $\frac{15}{17}$.
Use the pythagorean theorem to find the opposite side of $\theta$.
$17^2=15^2+opp^2$
$opp^2=289-225=64$
$opp=8$
$sin~\theta=\frac{opp}{hyp}=\frac{8}{17}$
$tan~\theta=\frac{opp}{adj}=\frac{8}{15}$
$cot~\theta=\frac{adj}{opp}=\frac{15}{8}$
$sec~\theta=\frac{hyp}{adj}=\frac{17}{15}$
$csc~\theta=\frac{hyp}{opp}=\frac{17}{8}$
