Final answer:
The distance between Noi and Poi can be found using the Law of Cosines, and the total distance between Moi and Poi can be calculated by adding the distance between Moi and Noi to the distance between Noi and Poi.
Step-by-step explanation:
The distance between Noi and Poi can be determined using the given information. The boat sails 69° west of north from Noi to Poi, and on its return leg from Poi, it sails 28° east of south. To find the distance between Noi and Poi, we need to use the Law of Cosines, which states that c^2 = a^2 + b^2 - 2ab*cos(C), where c is the distance between Noi and Poi, a is the distance from Noi to the origin, and b is the distance from Poi to the origin. In this case, a = 4.76 nmi and b = 4.76 nmi. We can use the formula to find the distance between Noi and Poi: c^2 = 4.76^2 + 4.76^2 - 2(4.76)(4.76)cos(180° - (69° + 28°)). After determining the value of c, we can convert it to kilometers by multiplying it by the conversion factor 1852 m/nmi.
The distance between Moi and Poi can be determined in a similar way. We need to find the distance from Moi to Noi and add it to the distance between Noi and Poi. From the given information, we know that Moi is 39° north of east from the origin, and Noi is 37° north of east from the origin. Using the Law of Cosines, we can determine the distance between Moi and Noi: d^2 = 4.76^2 + 4.76^2 - 2(4.76)(4.76)cos(180° - (37° + 39°)). After determining the value of d, we can calculate the total distance between Moi and Poi by adding the distance between Moi and Noi to the distance between Noi and Poi. Again, we can convert the distance to kilometers by multiplying it by the conversion factor 1852 m/nmi.