Answer
$b=\sqrt {91}$
$\sin B=\frac{\sqrt {91}}{10}$
$\cos B=\frac{3}{10}$
$\tan B=\frac{\sqrt {91}}{3}$
$\csc B=\frac{10\sqrt {91}}{91}$
$\sec B=\frac{10}{3}$
$\cot B=\frac{3\sqrt {91}}{91}$
Work Step by Step
$b=\sqrt {c^{2}-a^{2}}=\sqrt {10^{2}-3^{2}}=\sqrt {91}$
$\sin B=\frac{\text{side opposite}}{\text{hypotenuse}}=\frac{b}{c}=\frac{\sqrt {91}}{10}$
$\cos B=\frac{\text{side adjacent}}{\text{hypotenuse}}=\frac{a}{c}=\frac{3}{10}$
$\tan B=\frac{\text{side opposite}}{\text{side adjacent}}=\frac{b}{a}=\frac{\sqrt {91}}{3}$
The cosecant, secant, and cotangent ratios are reciprocals of the sine, cosine, and tangent values, respectively, so we have
$\csc B=\frac{10}{\sqrt {91}}=\frac{10\sqrt {91}}{91}$
$\sec B=\frac{10}{3}$
$\cot B=\frac{3}{\sqrt {91}}=\frac{3\sqrt {91}}{91}$
