Answer
1.776815
Work Step by Step
Converting $145^{\circ}45'$ to decimal degrees, we get
$145^{\circ}45'=145^{\circ}+\frac{45}{60}^{\circ}=145^{\circ}+0.75^{\circ}=145.75^{\circ}$
$\csc 145^{\circ}45'=\csc 145.75^{\circ}$
Now, we use the reciprocal identity $\csc\theta=\frac{1}{\sin\theta}$ to simplify the expression.
$\csc 145.75^{\circ}=\frac{1}{\sin 145.75^{\circ}}\approx1.776815$
