Let x be the length of AC and 7x be the length of AB.

According to the given ratio, AC/AB = 2/7, which means x/7x = 2/7.

Solving for x:
x/7x = 2/7
1/7 = 2/7
1 = 2

This shows that there is an error in the given ratio. Let's assume the correct ratio is AC:AB = 7:2.

Now, AC:AB = 7:2
AC = 7x
AB = 2x

Given that BC = 10, we can find the length of AC and AB:
7x + 2x = 10
9x = 10
x = 10/9

So, the length of AC is:
AC = 7x = 7(10/9) = 70/9

And the length of AB is:
AB = 2x = 2(10/9) = 20/9

Therefore, the lengths of AC and AB are 70/9 and 20/9, respectively.