A plane flies 452 miles north and then 767 miles west.
What is the direction of the plane's resultant vector?
Hint: Draw a vector diagram.
\[
\theta=[?]^{\circ}
\]
Round your answer to the nearest hundredth.
Enter

Step 1 ：Represent the plane's northward and westward movements as two sides of a right triangle, with the resultant vector as the hypotenuse.

Step 2 ：The direction of the resultant vector can be found by calculating the angle between the northward vector and the resultant vector.

Step 3 ：This can be done using the tangent function, which is the ratio of the opposite side (the westward movement) to the adjacent side (the northward movement).

Step 4 ：The angle can be found by taking the arctangent of this ratio.

Step 5 ：Let the northward movement be 452 miles and the westward movement be 767 miles.

Step 6 ：Calculate the angle in radians as \(\theta_{rad} = \arctan\left(\frac{west}{north}\right) = \arctan\left(\frac{767}{452}\right)\).

Step 7 ：Convert the angle from radians to degrees to get \(\theta_{deg} = \theta_{rad} \times \frac{180}{\pi}\).

Step 8 ：Round the angle to the nearest hundredth to get \(\theta_{deg} = 59.49\).

Step 9 ：Final Answer: The direction of the plane's resultant vector is \(\boxed{59.49^{\circ}}\) west of north.