a Let's draw a diagram.

$Pedro$ starts from the camp $C,$ walks east $5$ miles to $P,$ turns $1 5^{\circ}$ south of east, and walks $2$ more miles to the waterfall $W$ .
$Joel$ starts from the camp $C,$ walks west $5$ miles to $J,$ turns $3 5^{\circ}$ north of west, and walks $2$ more miles to the lake $L .$

To compare the distances of the destinations from the camp, $C W$ and $C L,$ let's consider triangles $△ C P W$ and $△ C J L .$

The two triangles have two pairs of congruent sides.

Congruent Sides	Justification
$\overline{C P} ≅ \overline{C J}$	Both segments represent a $5$ kilometer walk.
$\overline{P W} ≅ \overline{J L}$	Both segments represent a $2$ kilometer walk.

Let's compare the angles at

P

and at

J .

We can find the measure of these angles using that they form a linear pair with the respective turning angles.

15 + m ∠ P = 180 35 + m ∠ J = 180 ⟹ m ∠ P = 165 ⟹ m ∠ J = 145

We now know that triangles

△ C P W

and

△ C J L

have two pairs of congruent sides, and the included angle in triangle

△ C P W

is larger than the included angle in triangle

△ C J L .

m ∠ P > m ∠ J

According to the Hinge Theorem, this implies that the third side of triangle

△ C P W

is longer than the third side of triangle

△ C J L .

C P > C L

When

Pedro

and

Joel

reach their destinations,

Joel

is closer to the camp.

Exercise 16 Page 376