MYSTERIES OF THE EQUILATERAL TRIANGLE - HIKARI Ltd

Chapter 3
Applications of the Equilateral
Triangle
Figure 3.1: Equilateral Triangle Method in Surveying [34]
Application 1 (Surveying). In surveying, the Equilateral Triangle Method
[34] is used to measure around obstacles.
With reference to Figure 3.1, point B is set on the transit line as near the
obstacle as practicable but so that a line BC at 60 ◦ with the transit line can be
run out. The instrument is then set up at B, backsighted on A, and an angle of
120 ◦ laid off. The line BC is made long enough so that, when the instrument
is set up at C and 60 ◦ is laid off from it, CD will lie outside the obstacle. BC
is measured and CD is made equal to BC. If now the instrument is set up at
D and angle ∠CDE laid off equal to 120 ◦ then the line DE is the continuation
of the original transit line and BD = BC.
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