
Applications
of Trigonometry 

Applications
of Trigonometry in Geodesy (or Plane Surveying) 
Applications in geodesy or plane
surveying 






Applications
of Trigonometry in Geodesy (or Plane Surveying)

Applications in geodesy or plane
surveying

In plane surveying of geographical features, boundaries and areas are determined by the measurement of
points and lines of direction on the earth's surface. Obtained horizontal and vertical distances and angles are then processed using computations based on geometry and trigonometry.


For example, to determine distance
x between points,
C
and
D, which cannot be measured directly, measured
is the distance
d
between accessible points A
and B
and angles
a_{1},
a_{2} and
b_{1},
b_{2}.

In
DABC,



and in DABD,


applying the cosine law in the triangle
ACD,






Example:
A ground in form of a quadrilateral should be divided into two equal areas, see
the below figure.

At what distance from the vertex C
dividing line segment AE
intersects the side BC
if lengths of sides are, b = 24 m,
c = 28 m and
d = 45 m, and angles
b = 57° and
d =
115°.

Solution: In
DACD,
e^{2} =
b^{2} + c^{2}  2bc
· cosd,
e = 43.9 m,


since b
+ e
+ j =
180°,
j =
180° 
(e
+ b) =
63°44′19″.




The area of the quadrilateral
ABCD as the sum of triangles
ACD
and
ABC,


The area of the triangle ABE
is required to be half of the area of the quadrilateral, thus











Geometry
and use of trigonometry contents  B 



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