Answer
$\sin\alpha=\frac{5}{13}$
$\cos\alpha=\frac{12}{13}$
$\tan\alpha=\frac{5}{12}$
$\csc\alpha=\frac{13}{5}$
$\sec\alpha=\frac{13}{12}$
$\cot\alpha=\frac{12}{5}$
Work Step by Step
Let $x$ be the length of the side with an unknown length.
Using Pythagorean Theorem to find $x$.
$x=\sqrt{13^{2}-5^{2}}$
$x=\sqrt{169-25}$
$x=\sqrt{144}$
$x=12$
$\sin\alpha=\frac{opposite}{hypotenuse}=\frac{5}{13}$
$\cos\alpha=\frac{adjacent}{hypotenuse}=\frac{12}{13}$
$\tan\alpha=\frac{opposite}{adjacent}=\frac{5}{12}$
$\csc\alpha=\frac{hypotenuse}{opposite}=\frac{13}{5}$
$\sec\alpha=\frac{hypotenuse}{adjacent}=\frac{13}{12}$
$\cot\alpha=\frac{adjacent}{opposite}=\frac{12}{5}$
