(Sept.Brain Twister)Puzzle Diagram and Solution: Posed to the meeting attendees by Tom Price- WB9UNG
A puzzle and associated diagram was presented to those in attendance at the club meeting.
The Puzzle: Given a distant object of unknown height AB, on the other side of a river from
your point of observation, determine the height, AB, and the distance, BC1, from the observer. *










A Solution*: (1) Place a pole of height H1 at position P1 on the ground, and establish the
position along the ground, C1, such that when sighting from point C1, the tip of the pole
just appears to graze the top of the object AB at point A. (2) Likewise, with a second
pole of height H2 at position P2 on the ground, establish the position along the ground,
C2, such that when sighting from point C2, the tip of the pole again appears to just
graze the top of object AB at point A. Measure lengths H1, H2, and distances P1C1, C1C2,
and P2C2. (3) Distance BC1 and the height AB can then calculated using the following two formulas:
BC1 = (H2) (C1C2) / ((H1/P1C1) - (H2/P2C2))
AB = (H1) (BC1) / (P1C1)
An interesting feature of the solution is that it does not use the Pythagorean Theorem (c^2=a^2+b^2),
nor does it use a table of Trig Tangents. A handout showing the details of the derivation
above formulas will be available at the next club meeting.

*Problem posed as an example of early Chinese Trigonometry in a diagram appearing on
p.98 of The Norton History of Mathematical Sciences, Ivor Grattan_Guiness;
W. W. Norton & Co., New York; 1998. ISBN 0-393-04650-8.
Solution steps and formulas developed by Tom Price (WB9UNG), author of this short note.

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