Answer
b = $\sqrt 13$
$\sin$B = $\frac{\sqrt 13}{7}$
$\cos$B = $\frac{6}{7}$
$\tan$B = $\frac{\sqrt 13}{6}$
$\csc$B = $\frac{7\sqrt 13}{3}$
$\sec$B = $\frac{7}{6}$
$\cot$B = $\frac{6\sqrt 13}{13}$
Work Step by Step
a = 6
c = 7
Pythagorean Theorem: c$^{2}$ = a$^{2}$ + b$^{2}$
Therefore:
7$^{2}$ = 6$^{2}$ + b$^{2}$
49 = 36 + b
b$^{2}$ = 49 - 36
b$^{2}$ = 13
b = $\sqrt 13$
Therefore:
$\sin$B = $\frac{opposite}{hypotenuse}$ = $\frac{b}{c}$ = $\frac{\sqrt 13}{7}$
$\cos$B = $\frac{adjacent}{hypotenuse}$ = $\frac{6}{7}$
$\tan$B = $\frac{opposite}{adjacent}$ =$\frac{\sqrt 13}{6}$
$\csc$B = $\frac{hypotenuse}{opposite}$ = $\frac{7}{\sqrt 13}$ = $\frac{7\sqrt 13}{3}$
$\sec$B = $\frac{hypotenuse}{adjacent}$ =$\frac{7}{6}$
$\cot$B = $\frac{adjacent}{opposite}$ = $\frac{6}{\sqrt 13}$ = $\frac{6\sqrt 13}{13}$
