Spherical Trigonometry (from Activity)

Question 1

Given a right spherical triangle with C = 90°, a = 72°27’ and b = 61°49’. Find the area of the spherical triangle if the radius of the sphere is 10 m.

Answer 1

82.64 mm²

Question 2

A spherical triangle has the following parts: C = 90°, c = 80°, and b = 54°. Compute angle A.

Answer 2

75.95°

Question 3

Find the area of a spherical triangle if C = 90°, c = 80°, b = 54°, and the radius of the sphere is 10 m.

Answer 3

71.87 m²

Question 4

The parts of a spherical triangle are a = 60°18’, b = 101°24’, and c = 75°36’. Compute angle C.

Answer 4

65°59’

Question 5

A spherical triangle has the following parts: B = 118°, c = 82°, and a = 54°. Compute b.

Answer 5

107.12°

Question 6

Given the coordinates of 2 places: New York( 40°43’ N, 74° 0’ W ) and Liverpool( 53° 24’ N, 3° 4’ W ). Find the distance between the 2 places, in nautical miles.

Answer 6

2, 870 N.M.

Question 7

Given the coordinates of 2 places: New York( 40°43’ N, 74° 0’ W ) and Liverpool( 53° 24’ N, 3° 4’ W ). Find the bearing of Liverpool from New York.

Answer 7

N 49° 30’ E

Question 8

Given the coordinates of 2 places: New York( 40°43’ N, 74° 0’ W ) and Liverpool( 53° 24’ N, 3° 4’ W ). If the time now in New York is 8:00 AM, what is the time in Liverpool?

Answer 8

12:44 PM

Question 9

An airplane flew from Sydney ( 151°12’ E, 33°52’ S ) on a course N 40° W and maintaining a uniform altitude. At what longitude will it crosses the equator?

Answer 9

126° 08’

Question 10

An airplane flew from Sydney ( 151°12’ E, 33°52’ S ) on a course N 40° W and maintaining a uniform altitude. What is its average speed if it crosses the equator 6 hours after it left Sydney?

Answer 10

412.20 knots