is 0. When the telescope is pointed up at a higher feature (elevated), the vertical angle increases from 0
and is called a plus vertical angle. These values increase from 0, to +90, when the telescope is pointed
straight up. As the telescope is depressed (pointed down), the angle also increases in numerical value.
A depressed telescope reading showing that it is below the horizontal plane is called a minus vertical
angle. These numerical values increase from 0, to -90, when the telescope is pointed straight down.
d. To determine the difference in elevation between two points, set up and level the instrument at
one point. Hold the rod at another point. Point the telescope at an easily read value (a full meter) on the
rod, and measure the vertical angle (Figure 4-12). Determine the horizontal distance (ED) between the
instrument and rod by taping, obtaining a stadia reading, or by triangulation. You may also determine
the slope distance (EB) using EDME. Whichever distance (ED or EB) is selected, one side and one
angle () of a right triangle should be determined. Using this information, compute the other sides and
angle. For trigonometric leveling, only the side opposite the measured angle, the difference in elevation,
is computed.
Figure 4-12. Trigonometric Leveling With the Telescope in an Elevated Position
(1) The computation consists of multiplying the measured distance by the proper trigonometric
function of the measured angle (sine, if the slope distance [EB] is measured; tangent, if the horizontal
distance [ED] is measured). Where AE is the height of the instrument above point A, and BC is the
height of the line of sight above point C, the difference in elevation between A and C is AE + BD - BC.
(2) This method of determining the difference in elevation should be limited to horizontal
distances less than 300 meters when moderate precision is sufficient and to proportionately shorter
distances when higher precision is required.
EN0593
4-26
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