Final answer:
To find the magnitude of the ship's resultant vector, we need to break down the given vectors into their north-south and east-west components. We can then add up these components separately and use the Pythagorean theorem to calculate the magnitude.
Step-by-step explanation:
To find the magnitude of the ship's resultant vector, we can use the concept of vector addition. First, we need to break down the given vectors into their north-south and east-west components. The ship sails 133 miles north, so the north-south component of this vector is 133 and the east-west component is 0. Then, the ship sails 229 miles at an angle of 20° east of north. We can find the north-south and east-west components of this vector using trigonometry. The north-south component is 229 * cos(20°) and the east-west component is 229 * sin(20°).
Next, we can add up the north-south and east-west components separately to get the resultant north-south and east-west components. To find the magnitude of the resultant vector, we can use the Pythagorean theorem. The magnitude is given by sqrt((north-south component)^2 + (east-west component)^2).
In this case, the north-south component is 133 + (229 * cos(20°)) and the east-west component is (229 * sin(20°)). Plugging in these values into the formula, we can calculate the magnitude of the ship's resultant vector.