The situation forms the right triangle above.
Since it is a right triangle we can apply the Pythagorean theorem:
c^2 = a^2 + b^2
Where:
C = hypotenuse (the longest side) = 15 ft
a & b = the other 2 legs of the triangle = 5 and x
Replacing:
15^2 = x^2 + 5^2
Solve for x
225 = x^2 + 25
225 - 25 = x^2
200 = x^2
√200 = x
x = 14.14 ft (height of the building)