From a port, a boat sails 5 miles bearing of 60° then 3 miles on a bearing of 120° Determine the distance and bearing required to return to the port

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

Thus, the distance and bearing required to return to the port are 7 miles.

More about the trigonometry link is given below,

link

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°

lockers 1, 4, 9, 16, 25, 40, and 49 are open

i ran through it by the other answer is wrong

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step-by-step explanation: