Solve the problem.
-A bird flies from its nest $6 \mathrm {~km}$ in the direction $11 ^ { \circ }$ north of east, where it stops to rest on a tree. It then flies $9 \mathrm {~km}$ in the direction $38 ^ { \circ }$ south of west and lands atop a telephone pole. With an xy-coordinate system where the origin is the bird's nest, the $x$-axis points east, and the $y$-axis points north, at what point is the tree located?
A) (5.890, 1.145)
B) (0.02655, -6.000)
C) (1.145, 5.890)
D) (0.9816, 0.1908)

Question

Quizplus · Accepted Answer

The bird's first flight can be broken down into its x (eastward) and y (northward) components using trigonometry. For the eastward (x) component: $6 \cos(11^\circ)$ and for the northward (y) component: $6 \sin(11^\circ)$. Calculating these gives approximately $5.890$ km east and $1.145$ km north, which corresponds to the coordinates $(5.890, 1.145)$.

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