\section{Indoor: Calibrate your hand to measure angles}

\subsection*{Materials} you, ruler, string

\subsection*{Instructions}

Sextants allow the precise measurement of angles, but not all of us
carry one in our back pocket (plus they take some practice). So you
are going to calibrate various parts of your hand to allow you to
measure angles.

Turn your head $90^\circ$ and extend your arm straight out from the
shoulder. Now extend your thumb like you're hitchhiking. This will be
one of your basic measuring devices. Now make a loose fist. There's
your other device.

\textbf{Record all your measurements, the estimate precision of each
  measurements and your calculations:}

Measure the width of your thumb across the nail. Use the string to
measure the distance from your eye to your thumb at arm's length. Get
as accurate a measurement as possible. Check how much difference it
makes if you hold your arm in front of you versus to the side, or move
your head slightly. Calculate the angle subtended by your thumb in
degrees, and estimate the precision of your measurement.

Repeat this process for your fist (across the knuckles.)

You now have two ``devices'' for estimating angles that are always
with you.

\section{Indoor: Another calibration of your hand for angle measurement}

\subsection*{Materials} you, ruler, string, paper, tape, hallway

\subsection*{Instructions}

\textbf{Record all your measurements, the estimate precision of each
  measurements and your calculations:}

This time go out in the hall and secure a meter stick to the wall
horizontally. Back up until your thumb held at arm's length spans five
to ten centimeters.

Without moving, count how many centimeters are spanned by your thumb
and by your fist held out at arms length, then get your lab partner to
use string to measure the distance from your eye to the meter
stick. Get measurements as accurate as you can, and estimate your
precision.

Calculate the angle subtended by your thumb and fist in degrees, and
estimate the precision of this value.

\textbf{Which measurement (this one, or the one from the previous
exercise) was more precise? Pick final values and precisions for the
angles spanned by your thumb and fist.}

\section{Indoor: Measure angles with your hand}

\subsection*{Materials} you, ruler, string, setup in hallway

\subsection*{Instructions}

Do the calibration exercises before this one.

I will put a line of tape on the floor in the hallway,
and will tape a ruler to the wall. From the line, measure the
angular width of the ruler using your thumb. 

Now check your results: \textbf{Get your partner's help in using the
string to measure the distance from your eye to the wall. Calculate
the angle that should be subtended by the ruler at that distance. How
well do your results agree? How does your accuracy compare to your
estimated precision?}

