Explanation:
we need Pythagoras and a little bit of open mind.
Pythagoras is
c² = a² + b²
with c being the Hypotenuse (side opposite of the 90° angle), a and b being the legs.
the incenter means that it is the center point of the inscribed circle (being totally inside the triangle and touching every side at exactly one point).
that means that
GF = GB = GD
but GF we know : 22
so, GB = 22
now we can use the right-angled triangle ABG to find AG :
AG² = AB² + GB²
AG² = 32² + 22² = 1024 + 484 = 1508
AG = sqrt(1508) = sqrt(4×13×29) = 2×sqrt(377) =
= 38.83297568...