Answer
C is a distance of 281.3 km from A
Work Step by Step
The points A, B, and C form a triangle.
The angle $B = 90^{\circ}- 51^{\circ}20'$ which is $38^{\circ}40'$
We can use the law of cosines to find the distance $AC$:
$AC^2 = AB^2+BC^2-2(AB)(BC)~cos~B$
$AC = \sqrt{AB^2+BC^2-2(AB)(BC)~cos~B}$
$AC = \sqrt{(450~km)^2+(359~km)^2-(2)(450~km)(359~km)~cos~38^{\circ}40'}$
$AC = \sqrt{79107.6~km^2}$
$AC = 281.3~km$
C is a distance of 281.3 km from A
