I don't really see how this pertains to Mathematics...
To answer this, we substitute 12 ft to the f(h) in the given equation,
f(h) = -8t² + 8t + 12 = 12
Subtracting 12 from both sides of the equation will give us an answer of,
-8t² + 8t = 0
Then, we transpose 8 to the other side and divide the equation by -8 and t, we get an answer of t = 1 second.
Based on the picture above,
The theorem or postulate that justifies that Angle HEF ~ angle HGE is :
A. AA similarity postulate
(s is used for equal side, that is used for congruent)
hope this helps