so, a full circle has 360°, thus when the minute hand does one hour, it does a full circle, therefore 360°.
now, how many degrees are there in 1 minute? well, there are 60 minutes in 360°, therefore there are 360/60 degrees in 1 minute, or 6°.
now, we know in 1 hour there are 360°, how many in 27 minutes? well, 27 * 6, or 162°. So after 1hr and 27min, the minute hand has done 360+162 or 522°.
we also know the minute hand is 2 inches long, thus
[tex]\bf \textit{arc's length}\\\\
s=\cfrac{\pi \theta r}{180}\quad
\begin{cases}
r=radius\\
\theta =angle~in\\
\qquad degrees\\
------\\
r=2\\
\theta =522
\end{cases}\implies s=\cfrac{\pi \cdot 522\cdot 2}{180}[/tex]
which is roughly 18 inches rounded up.
