SPHERICAL
TRIANGLE
TRIANGLE
The theodolite
measures horizontal angles in the horizontal plane, but when the area becomes
large, such as in the case of primary triangulation, the curvature of the earth
means that such planes in large triangles called as spherical triangles or
geodetic triangles are not parallel at the apices as shown in Fig. 6.8.
Accordingly, the three angles of a large triangle do not total 180°, as in the
case of plane triangles, but to 180° + £, where £ is known as spherical
excess. The spherical excess depends upon the area of the triangle, and it
is given by
measures horizontal angles in the horizontal plane, but when the area becomes
large, such as in the case of primary triangulation, the curvature of the earth
means that such planes in large triangles called as spherical triangles or
geodetic triangles are not parallel at the apices as shown in Fig. 6.8.
Accordingly, the three angles of a large triangle do not total 180°, as in the
case of plane triangles, but to 180° + £, where £ is known as spherical
excess. The spherical excess depends upon the area of the triangle, and it
is given by
£= Ao / R sin1’ seconds
where A =
the area of the triangle in sq km, and
the area of the triangle in sq km, and
R =
the mean radius of the earth in km (=6373
km).
the mean radius of the earth in km (=6373
km).
The triangular
error is given by
error is given by
£ = Σ Observed angles – (180° + £)
= A + B +
C – (180° – £)
C – (180° – £)
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