Question

A woman walks 100 yards east along a straight shoreline and then swims 30 yards south 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. (11.40, –88.28°) (104.40, –88.28°) (11.40, –16.70°) (104.40, –16.70°)

Answer 1

Using trigonometric ratio tangent
Tan θ = 30/100
θ = 16.70, but since it is in an anticlockwise direction it will be -16.7
using Pythagoras theorem
a²+b²=c²
thus, c²=100²+30²
c = √(100²+30²)
= 104.40.
Therefore,the current position coordinates will be
(104.40, -16.70°)