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UPSC Civil Service Exam Questions - Engineering

Q1:

The difference between the sum of the angles of a plane triangle and the sum of the angles of a spherical triangle is one second when the triangle on the earth surface has an area of about

A 105 sq.km.

B 135 sq.km.

C 159 sq.km.

D 195 sq.km.

ANS:D - 195 sq.km.

A x 180/ π*R = spherical excess in degrees where R=radius of earth and A=area of a spherical triangle.

Now for spherical excess (E) of 1 sec,
A = π*R^2*E/180x3600 = 195 km2.