The branch of mathematics that deals with the relationships between the
sides and the angles of triangles and the calculations
based on them, particularly the trigonometric
functions. Sherlock Holmes relies on a little trigonometry to solve
a 250-year-old mystery known as the Musgrave Ritual (in a short story of
the same name) – an enigmatic series of clues that refers to the shadow
of an elm tree when the sun is just visible at the top of a nearby oak to
point toward buried treasure. The great detective recalls to Watson his
conversation with Reginald Musgrave:
"Have you any old elms?" ...
"There used to be a very old one over yonder, but it was struck by lightening
ten years ago, and we cut down the stump."
"You can see where it used to be?"
"Oh, yes." ...
"I suppose it is impossible to find out how high the elm was?"
"I can give it you it at once. It was sixty-four feet.... When my old
tutor used to give me an exercise in trigonometry, it always took the
shape of measuring heights." ...
I went with Musgrave to his study and whittled myself this peg, to which
I tied this long string with a knot at each yard. Then I took two lengths
of a fishing-rod, which came to just six feet... The sun was just grazing
the top of the oak. I fastened the rod on end, marked out the direction
of the shadow.... It was nine feet in length. Of course, the calculation
was now a simple one. If a rod of six feet threw a shadow of nine, a tree
of sixty-four feet would throw one of ninety-six... I measured out the
distance ... and I thrust a peg into the spot.