Answer
(a) The distance between them is 22.7 meters.
(b) Ricardo should walk at an angle of $67.6^{\circ}$ south of east.
Work Step by Step
Let east and south be positive directions.
When they stop walking, Jane and Ricardo are at positions J and R respectively. Let $d$ be the vector that Ricardo needs to walk to go to Jane's position.
$d+R = J$
$d = J-R$
We can find the east component $d_x$ of $d$.
$d_x = -16.0~cos(30.0^{\circ})~m - (-26.0)~sin(60.0^{\circ})~m$
$d_x = 8.66~m$
We can find the south component $d_y$ of $d$.
$d_y = 16.0~sin(30.0^{\circ})~m - (-26.0)~cos(60.0^{\circ})~m$
$d_y = 21.0~m$
(a) We can use $d_x$ and $d_y$ to find the magnitude of $d$.
$d = \sqrt{(d_x)^2+(d_y)^2}$
$d = \sqrt{(8.66~m)^2+(21.0~m)^2}$
$d = 22.7~m$
(b) We can find the angle south of east.
$tan(\theta) = \frac{21.0}{8.66}$
$\theta = tan^{-1}(\frac{21.0}{8.66}) = 67.6^{\circ}$
Ricardo should walk 22.7 m at an angle of $67.6^{\circ}$ south of east.
