Answer:
(1000, 179°)
Step-by-step explanation:
In rectangular coordinates, where east is the +x direction and north is the +y direction, the woman's final position is (1000 yards west, 20 yards north) or (-1000, 20).
This is translated to polar coordinates (r, θ) using ...
r = √(x² +y²)
θ = arctan(y/x) . . . . with attention to quadrant
The magnitude of the distance (r) is ...
r = √((-1000)² +20²) = √1000400 ≈ 1000.2 ≈ 1000
θ = arctan(20/-1000) in quadrant 2, so is 180° -1.15° = 178.85° ≈ 179°
In polar coordinates, the final position is (1000, 179°).
