Answer
The distance from Winston-Salem to Goldsboro is 137 miles
Work Step by Step
The three cities form a triangle.
We can find the angle $C$ at Danville:
$C = 42^{\circ}+48^{\circ} = 90^{\circ}$
The triangle is a right triangle.
We can find the distance $a$ from Winston-Salem to Danville:
$a = (65~mph)(1.1~hr) = 71.5~mi$
We can find the distance $b$ from Danville to Goldsboro:
$b = (65~mph)(1.8~hr) = 117~mi$
We can find the distance $c$ from Winston-Salem to Goldsboro:
$c^2 = a^2+b^2$
$c = \sqrt{a^2+b^2}$
$c = \sqrt{(71.5~mi)^2+(117~mi)^2}$
$c = 137~mi$
The distance from Winston-Salem to Goldsboro is 137 miles
