This seems like a right triangle problem.
So assuming 14 feet is the hypotenuse and 4 feet is a leg of the right triangle, we can use the pythagorean theorem () to solve for the height of the house, in which we shall name it x.
So, the equation is .
Solve for x:
16+x^{2}= 196
x^{2}= 196-16
x^{2}= 180
x = 6√5 feet
Hope this helps!