Answer:
Distance = 7 miles
Bearing = 261.8°
Step-by-step explanation:
Using cosine rule :
b² = a² + c² - 2acCosB
b² = 3² + 5² - 2(3*5)Cos120
b² = 9 + 25 - 30cos120
b² = 34 + 15
b² = 49
b = 7
Bearing of A from C :
CosC = (a² + b² - c²) / 2ab
CosC = (9 + 49 - 25) / 2*3*7
CosC = 33 / 42
CosC = 0.785714
C = cos^-1(0.785714)
C = 38.2°
Henve, bearing to return to Port ;
(360 - (60 + 38.2)° = 261.8°
The relation of the cosine is used. Then the distance and bearing required to return to the port are 7 miles.
Trigonometry deals with the relationship between the sides and angles of a triangle.
From a port, a boat sails 5 miles bearing of 60° then 3 miles on a bearing of 120°.
The side of the triangle will be
AB = 5 and ∠A = 60°
BC = 3 and ∠B = 120°
Then by the cosine rule
[tex]\rm b^2 = a^2 + c^2 - 2ac \ cos B\\\\b^2 = 3^2 + 5^2 - 2*3*5*cos 120\\\\b^2 = 9 + 25 - 30 *(-0.5)\\\\b^2 = 34 + 15\\\\b^2 = 49\\\\b\ = 7[/tex]
Thus, the distance and bearing required to return to the port are 7 miles.
More about the trigonometry link is given below,
https://brainly.com/question/22698523
