Question

Starting at the island of Moi in an unknown archipelago, a fishing boat makes a round trip with two stops at the islands of Noi and Poi. It sails from Moi for 4.76nautical miles (nmi) in a direction 37 ∘north of east to Noi. From Noi, it sails 69 ∘ west of north to Poi. On its return leg from Poi, it sails 28 ∘east of south.

What distance does the boat sail between Noi and Poi? What distance does it sail between Moi and Poi? Express your answer both in nautical miles and in kilometers. Note: 1nmi=1852m.

a) 4.28nmi,9.52nmi,15.66km,17.56km
b) 4.28nmi,9.52nmi,15.66km,17.56km
c) 15.66km,17.56km,4.28nmi,9.52nmi
d) 17.56km,15.66km,9.52nmi,4.28nmi

Answer 1

The distance between Noi and Poi is 4.28 nmi. The distance between Moi and Poi is 9.52 nmi.

Step-by-step explanation:

To find the distance between Noi and Poi, we can break it down into two legs:
1. Leg from Noi to Poi: The boat sails 69° west of north for a certain distance, let's call it x.
2. Leg from Poi back to Noi: The boat sails 28° east of south for the same distance, x.

Since the boat made a round trip, the total distance between Noi and Poi is 2x. Now we need to find x.

Using the law of sines, we can write the following equation:

sin(28°) / x = sin(69°) / x

Simplifying this equation gives:

sin(28°) = sin(69°)

Therefore, x = 4.28 nmi.

The distance between Moi and Poi is the sum of the distances from Moi to Noi (4.76 nmi) and from Noi to Poi (2x).

So, the distance between Moi and Poi is 4.76 nmi + 2(4.28 nmi) = 9.52 nmi.

Converting to kilometers using the conversion factor 1nmi = 1852m, the distance between Noi and Poi is 4.28 nmi * 1852 m/nmi = 7,930.56 m = 7.93 km, and the distance between Moi and Poi is 9.52 nmi * 1852 m/nmi = 17,625.04 m = 17.63 km.