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12. A fisherman leaves his home port and heads in the direction N70°W. He travels 30 miles and reaches Egg Island. The next day, he sails N10°E for 50 miles, reaching Forrest Island. What is the distance between the fisherman\'s home port and Forrest Island to the nearest mile? a. he nearest tenth of a degree, what is the bearing from Forrest Island back to his home port?

Solution

Here
90° - 70° = 20 < right triangle North to South & East to West at Home.
90° - 10° = 80 < right triangle North to South & East to West at Egg. Angle of direction with respect to East West Line

80° + 20° (angle of approach) = 100° This make the Angle of Aproach & Angle of departure.
Cosine Law
Distance between Home & Forrest = HF
HF = [(30)² + (50)² - 2(30)(50) Cos 100°
HF = (900) + 2500 - 3000 (-0.17)
HF = (900) + 2500 + 520.95
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HF = 62.62 mi  
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b. Sine Law
Sin 100° / 62.62 = Sin / 30
Sin = 0.47
= 28.15°
Bearing of E (90°-28.15°)S
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Bearing from Forrest to home = E 61.85° S