See the two lines cutting the sides of the triangle? Connect them. Then the whole triangle will be similar to the little triangle on the top. So the sides are in proportionate measure to each other. Call the unknown distance x.

Thus:

(15 + 10)/15 = (9 + x)/9

25/15 = (9 + x)/9

5/3 = (9 + x)/9

9*5/3 = 9 + x

15 = 9 + x

x = 15 - 9 = 6 m.

-Dan