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Q: Which of the following angles has spherical excess?
  • A. 45º
  • B. 180º
  • C. 225º
  • D. 135º
Correct Answer: Option C - Spherical excess–In triangulation of a small area with sides of the triangles less than 3.5 km, the triangles are considered to be plane. But in a geodetic survey, the curvature of the earth is given due consideration and the sides of triangles are considered to be arcs. The sum of three angles will always be more than 180º by an amount known as spherical excess. Spherical excess = (180º + ε) • Hence, the given angles are 45o, 180º and 135º have No spherical excess, but 225º have the spherical excess.
C. Spherical excess–In triangulation of a small area with sides of the triangles less than 3.5 km, the triangles are considered to be plane. But in a geodetic survey, the curvature of the earth is given due consideration and the sides of triangles are considered to be arcs. The sum of three angles will always be more than 180º by an amount known as spherical excess. Spherical excess = (180º + ε) • Hence, the given angles are 45o, 180º and 135º have No spherical excess, but 225º have the spherical excess.

Explanations:

Spherical excess–In triangulation of a small area with sides of the triangles less than 3.5 km, the triangles are considered to be plane. But in a geodetic survey, the curvature of the earth is given due consideration and the sides of triangles are considered to be arcs. The sum of three angles will always be more than 180º by an amount known as spherical excess. Spherical excess = (180º + ε) • Hence, the given angles are 45o, 180º and 135º have No spherical excess, but 225º have the spherical excess.