MARCH 2020
A= 30°N 060°E
B= 50°S 155°E
Dlat- 80°S dlong- 95° E
Cos AB = Cos 95°Sin120°Sin40° + Cos 120°Cos 40°
AB = 115° 33.9’ = 6933.9 miles
Cos A = Cos 40° -Cos 120°Cos 115°33.9’
Sin 120° Sin 115°33.9’
A = 45.3° ~45°13.3’
Course initial = 134.7° T
Cos B =Cos 120° - Cos 40° Cos 115°33.9’
Sin 40° Sin 115° 33.9’
B = 106.9° T final course
Vertex lies outside:
Sin(90-PA)= Tan(90-P) Tan(90-A)
Tan(90-P)= Sin(90-PA) / Tan(90-A)
P = 116°44.6’
Longitude of vertex = 176° 44.6E
Sin (PO)=Cos(90-PA) Cos(90-A)
PO = 37°56’
Latitude: 52°4’S
Jan 2020 (PM)
A= 15° S 012°E
B=07°N 053°W
Dlat- 22°N Dlong- 65°W
Cos AB = Cos 65°Sin 97° Sin 75° + Cos 97° Cos 75°
AB = 68° 3.6’ = 4083.6 miles
Cos A = Cos 97° -Cos 68°3.6’ Cos 75°
Sin 68° 3.6’ Sin 75°
A = 104.1° T
Course initital =255.9° T
Cos B = Cos 75° - Cos 97°Cos 68° 3.6’
Sin 97° Sin 68v 3.6’
B = 70.7°
Course final = 289.3°T
JAN 2020 (AM)
A= 56° 45’N 065° 32’E
B= 33° 36’ N 132°20’E
Dlat- 23°09’ S Dlong- 66° 48’E
Cos AB =Cos 66°48’ Sin 33°15’ Sin 56° 24’ = Cos 33° 15’ Cos 56°24’
AB = 50° 0.4’ = 3000.4 miles
Cos A = Cos 56°24’ – Cos 33°15’Cos 50°0.4’
Sin 33°15’ Sin 50°0.4’
A = 87.8°T (initial course)~87°49.8’
Cos B= Cos 33°15’ – Cos 56°24’ Cos 50° 0.4’
Sin 56°24’ Sin 50° 0.4’
B = 41.1°
Course final = 138.9 ° T
Vertex inside:
Sin(90-PA) =Tan(90-P) Tan(90-A)
Tan(90-P) =Sin(90-PA)/ Tan(90-A)
P = 2°35.7°
Longitude of vertex = 068°7.7’E
Sin PO = Cos (90-PA) Cos( 90-A)
PO = 33°13.3’
Latitude of vertex = 56° 46.7’ N
3rd September 2019-
LAT - 38° 30’S
LONG – 025 ° 30’W
Cos A = CosPB – CosAB* CosAP
Sin AB *Sin AP
CosPB = Cos A* Sin AB *Sin AP + Cos AB*Cos A
CosPB = Cos 30 Sin 16°40’ Sin 51°30’ + Cos16°40’Cos51°30’
PB = 37°44.7’
Latitude final = 90°-PB = 90° - 37°44.7’
= 52°15.3’ S
Cos P =Cos AB –Cos AP Cos PB
Sin AP Sin PB
Cos P = 13°32.9 ‘ W = Dlong
Longitude final = 039°2.9’ W
Final course
Cos B = Cos 51°30’ –Cos 16°40’ Cos 37°44.7’
Sin 16°40’ Sin 37° 44.7’
B= 140.3
Final course = 360° - 140.3°
= 219.7° T
3rd September 2019-
A=77°08’S 166° 30’E
B=37° 49’ S 122° 25’ W
Dlat= 114° 57’ N Dlong- 71°05’ W
Cos P = Cos AB – Cos PB Cos PA
Sin PB Sin PA
Cos AB = Cos P Sin PB Sin PA + Cos PB Cos PA
= Cos 71° 05’ Sin 127° 49’ Sin 12° 52’ + Cos 127° 49’ Cos 12° 52’
= 122° 43.9’ = 7363.9 miles
Cos A = Cos 127°49’ – Cos 12°52’ Cos 122°43.9’
Sin 12°52’ Sin 122°43.9’
A = 117.3 ° ~117°19.9’
Course = 180° + 117.3° = 297.3°T°
Cos B = Cos 12°52’ – Cos 122°43.9’ Cos 127° 49’
Sin 122°43.9’ Sin 127°49’
B = 14.5° T
Course = 360° - 14.5°
= 345.5° T
vertex outside
Sin(90-PA) = Tan (90-P) Tan (90-A)
Tan(90 –P)= Cos PA / Tan( 90-A)
P= 27°55.8’
Long = 138°34.2’ E
Sin P = Cos (90-A) Cos( 90 – PA)
PO = 11°24.6’
Latitude = 78° 35.4 ‘ S
10th JULY 2019
10° N 040° E
30° N 100° E
Dlat-20°N Dlong- 60° E
Cos P= Cos AB- CosAP CosPB
Sin AP Sin PB
Cos AB = Cos 60° Sin 80° Sin 60° + Cos 80°Cos 60°
AB = 59°7.1’ = 3547.1’
Cos A = Cos 60° -Cos 80°Cos 59°7.1
Sin 80° Sin 59° 7.1’
A = 60.9°
= 60.9° T
Cos B = Cos 80° - Cos 60°Cos59°7.1’
Sin 60°Sin 59°7.1’
B = 96.4°
final course = 180°-96.4° = 83.6° T
6th MAY 2019
A = 25°15’ N 045°12’E
B = 10° 40 ‘N 130°20’E
Dlat- 14°35’ S Dlong- 085°08’E
Cos AB = Cos 85°8’ Sin 64°45’Sin 79°20’ + Cos 64°45’ Cos 79°20’
AB = 81°7.2’ = 4867.2’
Cos A = Cos 79°20’-Cos 64°45’Cos 81°7.2’
Sin 64°45’ Sin 81°7.2’
A = 82.3°T (initial course)
Cos B = Cos64°45’ – Cos79°20Cos 81°7.2’
Sin 79°20’Sin 81°7.2’
B = 65.8°
Course final = 180° - 65.8°
= 114.2° T
6th MARCH 2019
A= 35°40 ‘N 141°00’E
B= 45° 00 ‘N 174° 51.8’ E
Dlat- 9°20’ N Dlong - 44°8.2’ W
Cos P = Cos AB-CosPA Cos PB
Sin PA Sin PB
Cos AB = Cos 44°8.2’ Sin 54° 20’ Sin 45° + Cos 54°20’ Cos 45°
AB = 34° 27.3’ = 2067.3
Cos A = Cos 45° -Cos 54°20’ Cos 34° 27.3’
Sin 54° 20° Sin 34° 27.3’
A = 60° 30.1 = 60.5°T (initial course).
Cos B = Cos 54° 20’- Cos 45° Cos 34° 27.3°.
Sin 45° Sin 34° 27.3°.
B = 89.9 °
Final course = 180° - 89.9 = 90.1° T.
3rd Jan 2019
A=37° S 019°E
B=56°S 067° W
Cos AB = Cos 86°Sin 34° Sin 53° + Cos 34°Cos 53°
AB = 57°59.4’ =3479.4 miles
Cos A = Cos 34°- Cos 57°59.4’Cos 53°
Sin 57°59.4’ Sin 53°
A = 41° 8.2’
= 180° + 41°8.2’ = 221.1 ° T
Cos B = Cos 53° -Cos 57°59.4’ Cos 34°
Sin 57° 59.4° Sin 34°
B = 69° 58.5 = 69.9 ° T.
= 290.1° T(360° - 69.9°)
Vertex inside
Sin(90-PB)= tan(90-B) tan(90-P).
Sin(90-PB)/tan(90-B) = tan(90-P)
P= 23°43.9’’
Longitude of vertex = 043°16.1’W
Sin PO= cos (90-B) Cos(90-PB)
Sin PO = Cos(90-69.9) Cos( 90-34).
PO = 31°41.3’
Lat of vertex = 58°18.7’ S
2ND NOV 2018
A= 49° 50’N 005° 15’W
B= 32°29’N 064° 00 ‘W
Dlat- 17°21’ S Dlong- 58°45’W
Cos AB = Cos 58°45’ Sin 57°31’Sin 40°10’ + Cos 57°31’ Cos 40°10’
AB = 46° 9.5’ = 2769.5 miles
Cos A =Cos 57°31’- Cos 40°10’ Cos 46°9.5°
Sin 40°10’ Sin 46° 9.5’
A = 89.1°
Course initial = 270.9° T (360-89.1)
Cos B = Cos 40°10° - Cos 57°31’ Cos 46°9.5’
Sin 57° 31’ Sin 46°9.5’
B = 49.9°
Final course = 229.9° T (180+ 49.9)
5th September 2018
A= 25°15’ N 045°12’E
B= 10°40’N 130°20’E
Dlat- 14°35’ S dlong- 85°08’ E
Cos AB= Cos 85°08’Sin 64°45’Sin 79°20’ + Cos 64°45’ Cos 79°20’
AB = 81°7.2’ = 4867.2 miles
Cos A = Cos 79°20’ – Cos 64°45’Cos 81°7.2’
Sin 64°45’ Sin 81°7.2’
A = 82.3 ° T
Cos B=Cos64°45’-Cos79°20’Cos81°7.2’
Sin 79°20’ Sin 81°7.2’
B = 65.8°
Course final = 180° - 65.8° = 114.2° T
3rd July 2018
A= 07°N 053°W
B= 15°S 012°E
Dlat-22°S dlong -65°E
Cos AB =Cos 65°Sin97° Sin 75° + Cos75°Cos 97°
AB = 68° 3.6’ = 4083.6 ‘
Cos A = Cos 75° - Cos 68°3.6’ Cos 97°
Sin 68°3.6’ Sin 97°
A = 70.7°
Course = 109.3° T
Cos B= Cos 97°- Cos75°Cos 68°3.6’
Sin75°sin68°3.6’
B = 104.1° T = final course
3rd MAY 2018 / JAN 2017
Cos A = Cos PB –Cos PA Cos AB
Sin PA Sin AB
Cos 30 = Cos PB –Cos 16°40’ Cos 51°30’
Sin 16°40 Sin 51°30’
Cos PB = Cos 30°Sin 16°40’ Sin 51°30’ + Cos 16°40 Cos 51°30’q
PB = 37° 44.7’
Latitude arrived = 90° -37°44.7’ = 52°15.3’ S
Cos P = Cos 16°40’ – Cos 37°44.7’ Cos 51°30’
Sin 37°44.7’ Sin 51°30’
P = 13°32.9’
Arrival longitude = 39°2.9 ‘ W.
Cos B= Cos51°30’-Cos 16°40’Cos 37°44.7’
Sin16°40’ Sin 37°44.7’
B = 140°15.8’
Final course = 219.7°T
6th MARCH 2018
A= 10°N 40°E
B= 30°N 100°E
Dlat- 20°N Dlong- 60°E
CosAB = Cos 60° Sin 80° Sin 60° + Cos 80° Cos 60°
AB = 59° 7.1’ = 3547.1 miles
Cos A = Cos 60° - Cos 80° Cos 59° 7.1’
Sin 80° Sin 59° 7.1’
A = 60.9° T
Cos B = Cos 80° - Cos 60° Cos 59°7.1’
Sin 60° Sin 59° 7.1’
B = 96.4°
Course = 180 – 96.4 = 83.6° T
6Th SEPTEMBER 2017
A= 30° N 085° E
B= 42° N 110° E
Dlat- 12° N Dlong- 25° E
Cos AB = Cos 25° Sin 48° Sin 60° + Cos 48° Cos 60°
AB = 23°23.2’ = 1403.18 miles
Cos A = Cos 48° -Cos 60° Cos 23°23.2’
Sin 60° Sin 23° 23.2’
A = 52.3 ° T
Cos B = Cos 60° - Cos 48° Cos 23°23.2’
Sin 48° Sin 23°23.2°
B = 112.7°
Course final = 180-112.7 = 67.3 °T
7th NOVEMBER 2017
A= 56° S 067°W
B= 37° S 019°E
Dlat- 19°N dlong- 86°E
Cos AB= Cos 86° Sin 34° Sin 53° + Cos 34°Cos 53°
AB = 57°59.4 ‘ = 3479.4 miles
Cos A =Cos 53° - Cos 34° Cos 57°59.4’
Sin 34° Sin 57° 59.4’
A = 69.9°
Course initial = 110.1°T
Cos B = Cos 34° -Cos 53° Cos 57° 59.4’
Sin 53° Sin 57° 59.4’
B = 41.1 ° T = final course
JULY 2017 (PM)
A= 10°S 150° W
B= 40° N 160° E
Dlat- 50°N Dlong- 50°E
Cos AB = Cos 50°Sin 100°Sin50° + Cos 100°Cos 50°
AB = 68° 4.8’ = 4084.8’
Cos A = Cos 50° -Cos 100° Cos 68° 4.8’. It's 50 degree not 60 degree
Sin 100° Sin 68° 4.8’
A = 39.2° T
Cos B = Cos 100° - Cos 50° Cos 68° 4.8’
Sin 50° Sin 68° 4.8’
B = 125.6 °
Final course = 54.4° T
JULY 2017(AM)
A= 49°50’ N 005° 12’W
B= 13°06’N 059°20’W
Dlat-36°44’S dlong- 54°08’W
Cos AB= Cos 54°08’ Sin 40°10’ Sin 76°54’ + Cos 40°10’Cos 76°54’
AB = 57° 13.7’ = 3433.8 miles
Cos A = Cos 76°54’ – Cos 40°10’ Cos 57°13.7’
Sin 40°10’ Sin 57°13.7’
A = 110.2° T
Cos B = Cos40°10’ – Cos 76°54’Cos 57°13.7’
B = 38.4
= 180° + 38.4° = 218.4 ° T
MARCH 2017 (AM)
A= 19° N 067° W
B= 36° N 6°30’W
Dlat- 17°N Dlong-60° 30’ E
Cos AB = Cos 60°30’ Sin 71° Sin 54° + Cos 71° Cos 54°
AB = 55°23.2’ = 3323.2 miles.
Cos A = Cos 54°- Cos 71° Cos 55° 23.2’
Sin 71° Sin 55° 23.2’
A = 58.8° T~58°49.4’
Cos B = Cos 71° - Cos 54° Cos 55°23.2’
Sin 54° Sin 55°23.2’
B = 90.7 °
Course final = 89.3° T (180-90.7)
Vertex outside:
Sin(90-AP)= Tan(90-A) Tan(90-P)
Tan(90-P)= Sin(90-AP)/Tan(90-A)
= Sin(90-71)/tan(90-58.8)
P = 61°42.9’
Longitude of vertex=005°17.1’W
Sin PC = Cos(90-A)cos(90-AP)
PC = 53°59.7’
Latitude of vertex = 90° - 53° 58.5’ = 36°0.3’ N
MARCH 2017 (PM).
A= 20°30’ S 120° 15’E
B= 36°20’N 179°40’ E
Dlat- 56°50’N Dlong- 59° 25’E
Cos AB = Cos 59°25’Sin 110°30’ Sin 53°40’ + Cos 110°30’ Cos 53°40’
AB = 79°50.3’ = 4790.3 miles
Cos A = Cos 53°40’- Cos 110°30’ Cos 79°50.3’
Sin 110°30’ Sin 79° 50.3’
A = 44.8° T
Cos B =Cos 110°30’ – Cos 53°40 Cos 79° 50.3’
Sin 53°40’ Sin 79° 50.3’
B = 124.9° ~ 124°59.6’
Course = 55.1°T (180-124.9)
Vertex lies outside:
In small traiangle b= 180-124°59.6’=55°0.4
Tan(90-P) = Sin(90-PB) / Tan(90-B)
P = 49°45.4’
Longitude of vertex= 130°34.6’W
Sin PO = Cos(90-PB) Cos(90-B)
PO = 41°17.8’
Latitude of vertex = 48°42.2’N
MAY 2017 (AM)
A= 30° N 060°E
B= 50° S 155°E
Dat- 80°S Dlong-95°E
Cos AB =Cos 95° Sin 120° Sin 40° + Cos 120° Cos 40°
AB = 115° 33.9’ = 6933.9 miles
Cos A = Cos 40° - Cos 120° Cos 115° 33.9°
Sin 120° Sin 115° 33.9’
A = 45.2°
Course = 134.8° T
Cos B =Cos 120° - Cos 40° Cos 115 ° 33.9’
Sin 40° Sin 115° 33.9’
B = 106.9 ° T
Vertex outside:
Sin (90-AP) =Tan (90-p) tan(90-A)
Tan(90-P) = Sin(90-AP)/ Tan( 90-A)
P =116° 43.5’
Longitude of vertex = 176° 43.5’ E
Sin PC = Cos (90-AP) Cos (90-A)
AC = 37° 54.9 ‘
Latitude of vertex = 52° 5.1’S
MAY 2017 (PM)
A= 08° 15’N 078° 00’E
B= 33°50’S 025°30’E
Dlat- 42°05’ S Dlong- 52°30’W
Cos AB =Cos 52°30’ Sin 56°10’ Sin 98°15’ + Cos 56°10’ Cos 98°15’
AB = 65° 7.9’ = 3907.9 miles
Cos A = Cos 56° 10’ – Cos 98°15’ Cos 65° 7.9’
Sin 98° 15’ Sin 65° 7.9’
A = 46.6 °
Course initial = 226.6° T
Cos B= Cos 98°15’ –Cos 56°10’ Cos 65°7.9’
Sin 56° 10’ Sin 65° 7.9’
B = 120.1°
Course final = 239.9° T (360-B)
NOVEMBER 2016
A= 56° 45’N 065° 32’E
B= 33° 36’ N 132°20’E
Dlat- 23°09’ S Dlong- 66° 48’E
Cos AB =Cos 66°48’ Sin 33°15’ Sin 56° 24’ = Cos 33° 15’ Cos 56°24’
AB = 50° 0.4’ = 3000.4 miles
Cos A = Cos 56°24’ – Cos 33°15’Cos 50°0.4’
Sin 33°15’ Sin 50°0.4’
A = 87.8°T (initial course)~ 87°49.8’
Cos B= Cos 33°15’ – Cos 56°24’ Cos 50° 0.4’
Sin 56°24’ Sin 50° 0.4’
B = 41.1°
Course final = 138.9 ° T
Vertex inside:
Sin(90-PA) =Tan(90-P) Tan(90-A)
Tan(90-P) =Sin(90-PA)/ Tan(90-A)
P = 2°35.7’
Longitude of vertex = 068° 7.7’ E
Sin PO = Cos (90-PA) Cos( 90-A)
PO = 33°13.3’
Latitude of vertex = 56° 46.7’ N
SEPTEMBER 2016
A= 06° N 079° W.
B= 38° S 175° E
DLAT-44°S DLONG-106°E
Cos AB = Cos 106° Sin 96° Sin 52° + Cos 96° Cos 52°.
AB = 106°16.9’ = 6376.9 miles
Cos A = Cos 52°- Cos 96° Cos 106°16.9’
Sin 96° Sin 106°16.9’
A = 52.1°
Initial course = 127.9 ° T
Cos B = Cos 96°- Cos 52° Cos 106° 16.9’
Sin 52° Sin 106° 16.9’
B = 84.8°
Final course = 84.8° T
JULY 2016
A= 20° N 075°W
B= 45°N 050°W
Dlat- 25°N Dlong- 25°W
Cos AB= Cos 25°Sin 70°Sin 45°+ Cos 70° Cos 45°
AB = 32°25.7’ = 1945.7’
Cos A = Cos 45°- Cos 70° Cos 32°25.7’
Sin 70° Sin 32°25.7’
A = 33.9°T
Cos B = Cos 70°- Cos 45°Cos 32°25.7’
Sin 45° Sin 32°25.7’
B = 132.2°
Final course= 47.8° T
MAY 2016
A= 24° N 074° E
B= 48° N 145° 18’E
Dlat - 20° N Dlong- 70°48’E
Cos AB= Cos 78° 48’ Sin 66° Sin 42° + Cos 66° Cos 42°
AB = 59° 46.9’ =3586.9 miles
Cos A = Cos 42° - Cos 66° Cos 59° 46.9’
Sin 66° Sin 59° 46.9’
A = 46.9 ° T(initial course)
Cos B= Cos 66° -Cos 42° Cos 59° 46.9°
Sin 43° Sin 59° 46.9’
B = 86.8°
Final course = 93.2° T
MARCH 2016
A= 56° 45’N 065° 32’E
B= 33° 36’ N 132°20’E
Dlat- 23°09’ S Dlong- 66° 48’E
Cos AB =Cos 66°48’ Sin 33°15’ Sin 56° 24’ = Cos 33° 15’ Cos 56°24’
AB = 50° 0.4’ = 3000.4 miles
Cos A = Cos 56°24’ – Cos 33°15’Cos 50°0.4’
Sin 33°15’ Sin 50°0.4’
A = 87.8°T (initial course)~ 87°49.8°
Cos B= Cos 33°15’ – Cos 56°24’ Cos 50° 0.4’
Sin 56°24’ Sin 50° 0.4’
B = 41.1°
Course final = 138.9 ° T
Vertex inside:
Sin(90-PA) =Tan(90-P) Tan(90-A)
Tan(90-P) =Sin(90-PA)/ Tan(90-A)
P = 2°35.7°
Longitude of vertex = 068°7.7’E
Sin PO = Cos (90-PA) Cos( 90-A)
PO = 33°13.3’
Latitude of vertex = 56° 46.7’ N
JAN 2016
A= 24° N 074°15’W
B= 46°N 053°45’W
Dlat=22°N Dlong- 20°30’ E
Cos AB= Cos 20°30°Sin 66° Sin 44° + Cos 66° Cos 44°
AB = 27° 30.1’ = 1650.1 miles
Cos A = Cos 44°- Cos 66° Cos 27°30.1’
Sin 66° Sin 27°30.1’
A = 31.8° T
Cos B = Cos 66° -Cos 44° Cos 27° 30.1’
Sin 44° Sin 27° 30.1’
B = 136.1 °
Course final =43.9° T