Answer
$$h= 24\ ft$$
Work Step by Step
The Pythagorean Theorem states that for a right triangle:
$$ a^2+b^2=c^2$$
Where c is the length of the hypotenuse. Thus, the missing length is:
$$ 50^2 = 44^2 + h^2 \\ 2500= 1936 + h^2 \\ h= 24\ ft$$