Answer
$(a)\space 64\space m$
$(b)\space 37^{\circ}\space -south\space of\space east$
Work Step by Step
Please see the attached image first.
The magnitude of the displacement $r$ of the chimpanzee gives the shortest distance between the tree and the termite mound.
(a) By using the Pythagorean theorem, we can get
$r^{2}=(51\space m)^{2}+(39\space m)^{2}=4122\space m^{2}$
$r=\sqrt {4122}\space m=64\space m$
(b) We can write,
$tan\theta=\frac{39}{51}=0.76=\gt \theta=tan^{-1}(0.76)=37^{\circ}\space south\space of\space east$
