Answer
$\csc$ 30$^{\circ}$ = 2
Work Step by Step
$\csc$ 30$^{\circ}$
We must find side $x$ of the 30$^{\circ}$ - 60$^{\circ}$ Right Triangle.
Pythagorean Theorem: $c$$^{2}$ = $a$$^{2}$ + $b$$^{2}$
2$^{2}$ = 1$^{2}$ + $x$$^{2}$
4 = 1 + $x$$^{2}$
x$^{2}$ = 3
x = $\sqrt 3$
Now consider the triangle from the perspective of the 30$^{\circ}$ angle.
Hypotenuse = 2
Opposite = 1
Adjacent = $\sqrt 3$
$\tan$ 30$^{\circ}$ = $\frac{Hypotenuse}{Opposite}$ = $\frac{2}{1}$ = 2
Therefore:
$\csc$ 30$^{\circ}$ = 2
