#### Answer

The distance from Atlanta to Augusta is 87 miles

#### Work Step by Step

The three cities form a triangle.
We can find the angle $C$ at Macon:
$C = 27^{\circ}+63^{\circ} = 90^{\circ}$
The triangle is a right triangle.
We can find the distance $a$ from Macon to Augusta:
$a = (62~mph)(1.25~hr) = 77.5~mi$
We can find the distance $c$ from Atlanta to Augusta:
$\frac{a}{c} = sin~63^{\circ}$
$c = \frac{a}{sin~63^{\circ}}$
$c = \frac{77.5~mi}{sin~63^{\circ}}$
$c = 87~mi$
The distance from Atlanta to Augusta is 87 miles