Steve Lelievre suggested using arc tan 1/4 to find 15 degrees "in
emergency".
A slightly better approximation is to go via
sin(15) = 0.2588 and arcsin(0.25) = 14.4775 deg
cf. tan(15) = 0.2679 and arctan(0.25) = 14.0362 degrees
So, take your string and find a quarter of its length as before by two
halvings. Start from the centre point and mark a point on a first line at
the string's length away. From that point draw an arc (or mark a few points
to indicate it) using the quarter string as radius. Go back to the centre
and take the tangent to that arc as the second line.
The angle subtended is arcsin 0.25 or about 14 degrees 29 minutes, close
enough for practical purposes I would think.
If you want to get still closer, then do it both ways and add the difference
between them to the larger of the two angles to get 14 degrees 55 minutes.
(And if you dislike estimating the addition to make rather than constructing
it, then take two of the sine angles one after the other i.e. added together
and go back one of the tan angles to subtract it.)
Or of course you could just use the same process, with half the string
length instead of a quarter, to go via arcsin 1/2 and obtain 30 degrees,
then take the string and mark two points equidistant from the origin on the
two lines 30 degrees apart, and use doubling the string to find the point
midway between those two - hence bisecting the angle into two angles of
exactly 15 degrees with no error at all. But we're getting close to
terrestrial origami I fear ...
Regards
Andrew James
51 04 W
01 18 N
