Solve the problem.
-A bird flies from its nest 2 km in the direction 39° north of east, where it stops to rest on a tree. It then flies 5 km in the direction 13° 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) ( 1.259, 1.554)
B) ( 1.554, 1.259)
C) ( 0.5333, 1.928)
D) ( 0.7771, 0.6293)

Question

Quizplus · Accepted Answer

The bird's first flight can be broken down into x and y components using trigonometry. For the x-component: $2 \cos(39^\circ)$ and for the y-component: $2 \sin(39^\circ)$. Calculating these gives approximately 1.554 for the x-component (eastward) and approximately 1.259 for the y-component (northward). Therefore, the coordinates of the tree are (1.554, 1.259).

Solve the Problem. -A Bird Flies from Its Nest 2 Km in the Km