Spherical Trigonometry

Question 1

Set 2 Problem 49: An airplane flew from Sydney ( 151°12’ E, 33°52’ S ) on a course N 40° W maintaining a uniform altitude. At what longitude will it crosses the equator?

Answer 1

126°08’ E

Question 2

Set 3 Problem 25: 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 distance (in nautical miles) from Sydney when it crosses the equator?

Answer 2

2,473.20 NM (p. 45)

Question 3

Set 3 Problem 45: Given the parts of an oblique spherical triangle: A=121°, B=29°, and a=136°. Compute side c.

Answer 3

127.41° (p.49)

Question 4

Set 6 Problem 21: Find the area in sq. m. of a spherical triangle whose angles are 115°, 98°, and 82° if the radius of the sphere is 40 m.

Answer 4

3,211.40 m² (p.97)

Question 5

Set 6 Problem 48: 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 5

2,870 N.M. (p.101)

Question 6

Set 6 Problem 49: 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 6

N 49° 30’ E (p.101)

Question 7

Set 6 Problem 50: 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 New York from Liverpool.

Answer 7

N 75°08’ W (p. 102)

Question 8

Set 8 Problem 4: A spherical triangle has the following parts: B=118°, c=82°, and a=54°. Compute b.

Answer 8

107.12° (p.128)

Question 9

Set 8 Problem 22: Two cities 270 km apart lie on the same meridian. Find their difference in latitude if the earth’s radius is 3,960 km.

Answer 9

3/44 rad (p.131)

Question 10

Given a right spherical triangle with C=90°, a=72°27’, and b=61°49’.
Set 8 Problem 33: Find c.

Answer 10

81°49’ (p.133)

Question 11

Given a right spherical triangle with C=90°, a=72°27’, and b=61°49’.
Set 8 Problem 34: Find A.

Answer 11

74°25’ (p.133)

Question 12

Given a right spherical triangle with C=90°, a=72°27’, and b=61°49’.
Set 8 Problem 35: Find the area of the spherical triangle if the radius of the sphere is 10 m.

Answer 12

82.64 m^2 (p.134)

Question 13

Set 9 Problem 29: A right spherical triangle has the following parts: C=90°, a=40°, and b=80°. Find the measure of angle B.

Answer 13

83°32’ (p.150)

Question 14

Set 9 Problem 55: Compute angle A of a spherical triangle whose parts are: a=58°, b=112°, c=70°.

Answer 14

40°57’ (p.153)

Question 15

Set 9 Problem 55: Compute angle A of a spherical triangle whose parts are: a=58°, b=112°, c=70°.

Answer 15

40°57’ (p.153)