Answer
$\sin\alpha=\frac{\sqrt{11}}{4}$
$\cos\alpha=\frac{\sqrt{5}}{4}$
$\tan\alpha=\frac{\sqrt{11}}{\sqrt{5}}$
$\csc\alpha=\frac{4}{\sqrt{11}}$
$\sec\alpha=\frac{4}{\sqrt{5}}$
$\cot\alpha=\frac{\sqrt{5}}{\sqrt{11}}$
Work Step by Step
Let $x$ be the length of the side with an unknown length.
Using Pythagorean Theorem to find $x$.
$x=\sqrt{4^{2}-\sqrt5^{2}}$
$x=\sqrt{16-5}$
$x=\sqrt{11}$
$\sin\alpha=\frac{opposite}{hypotenuse}=\frac{\sqrt{11}}{4}$
$\cos\alpha=\frac{adjacent}{hypotenuse}=\frac{\sqrt{5}}{4}$
$\tan\alpha=\frac{opposite}{adjacent}=\frac{\sqrt{11}}{\sqrt{5}}$
$\csc\alpha=\frac{hypotenuse}{opposite}=\frac{4}{\sqrt{11}}$
$\sec\alpha=\frac{hypotenuse}{adjacent}=\frac{4}{\sqrt{5}}$
$\cot\alpha=\frac{adjacent}{opposite}=\frac{\sqrt{5}}{\sqrt{11}}$
