A ship traveled 60 miles due east and then adjusted its course 15 degrees northward. After traveling for a while, the ship turned back towards the port. The ship arrived in the port 139 miles later. What angle did the ship turn through when it headed back to the port? What is the total area that the ship covered during its journey? Round your angle to the nearest whole degree and the area to the nearest mile.

a. The angle that the ship turn through when it headed back to the port is 6.4°.

b. The total area that the ship covered during its journey 80.3 miles.

a. Angle

Let p represent the angle

Sin(180°-15°)/139=SinP/60

Sin165°/139=SinP/60

P=Sin^-1 (60sin165°/139)

P=6.4°

b. Total area covered

Let x represent the Total area covered

Hence:

Sin8.6°/x=Sin165°/139

x=80.3 miles

Inconclusion the ship turn at angle 6.4° and the total area is  80.3 miles.

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