Answer
c = 13
$\sin$$B$ = $\frac{12}{13}$
$\cos$$B$ = $\frac{5}{13}$
$\tan$$B$ = $\frac{12}{5}$
$\csc$$B$ = $\frac{13}{12}$
$\sec$$B$ = $\frac{13}{5}$
$\cot$$B$ = $\frac{5}{12}$
Work Step by Step
Pythagorean Theorem: c$^{2}$ = a$^{2}$ + b$^{2}$
a = 5
b = 12
Therefore:
c$^{2}$ = 5$^{2}$ + 12$^{2}$
c$^{2}$ = 25 + 144
c$^{2}$ = 169
c = $\sqrt 169$
c = 13
$\sin$$B$ = $\frac{opposite}{hypotenuse}$ = $\frac{b}{c}$ = $\frac{12}{13}$
$\cos$$B$ = $\frac{adjacent}{hypotenuse}$ = $\frac{a}{c}$ = $\frac{5}{13}$
$\tan$$B$ = $\frac{opposite}{adjacent}$ = $\frac{b}{a}$ = $\frac{12}{5}$
$\csc$$B$ = $\frac{hypotenuse}{opposite}$ = $\frac{c}{b}$ = $\frac{13}{12}$
$\sec$$B$ = $\frac{hypotenuse}{adjacent}$ = $\frac{c}{a}$ = $\frac{13}{5}$
$\cot$$B$ = $\frac{adjacent}{opposite}$ = $\frac{a}{b}$ = $\frac{5}{12}$
