The magnitude of the boats resultant vector is 314.1 mi
<h3>What is a vector?</h3>
A vector is a physical quantity that has both magnitude and direction.
<h3>What is a resultant vector?</h3>
A resultant vector is the sum of two or more vectors.
<h3>How to find the boats resultant vector?</h3>
Since the boat sails 285 miles south and then 132 miles west, we have that its first direction vector is r = (285 mi)j. Also, its direction vector west is r' = -(132 mi)i
So, the resultant vector R = r + r'
= (285 mi)j + (132 mi)i
= (132 mi)i + (285 mi)j
So, the magnitude of the resultant vector is R = √(r² + r'²)
So, substituting thevalues of the variables into the equation, we have
R = √(r² + r'²)
R = √((285 mi)² + (132 mi)²)
R = √(81225 mi² + 17424 mi²)
R = √(98649 mi²)
R = 314.08 mi
R ≅ 314.1 mi
So, the resultant vector is 314.1 mi
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(side opposite 30) ⇒ 
= 14.72 when rounded 2 decimal places