Question

A woman walks 200 yards west along a straight shoreline and then swims 50 yards north into the ocean on a line that is perpendicular to the shoreline. Using her starting point as the pole and the east direction as the polar axis, give her current position polar coordinates. Round the coordinates to the nearest hundredth. Express θ in degrees

Answer 1

r^2 = 200^2 + 50^2 = 42500
r = √42500 = 50√17

tanØ = -50/200 = -1/4
Ø = 165.96°

so using the (r,Ø) notation , her position is
(50√17, 165.96°)