Question 657291
First we will calculate the lengths in cm that the legs of the right triangle ABC have. Then, use the Pythagorean theorem to calculate the length of the hypotenuse of the right triangle which is the distance between A and C. It has to be a right triangle since since A is due west and C is due south of B.

If 1 cm = 10 km, 

AB=75 km/(10 km/cm)
AB=7.5 cm*km/km
AB=7.5 cm*1
AB=7.5 cm

BC=50 km/(10 km/cm)
BC=5 cm*km/km
BC=5 cm*1
BC=5 cm


Since the legs of the triangle have lengths of 5 and 7.5 cm, the distance AC is:

{{{a^2+b^2=c^2}}}
{{{5^2+7.5^2=c^2}}}
{{{25+56.25=c^2}}}
{{{81.25=c^2}}}
{{{sqrt(81.25)=c}}}
c=9.01 cm