To the nearest foot, how much farther up the building does the ladder now reach? show how you arrived at your answer

Here we have 2 right triangles with the same hypotenuses.  One "adjacent side" is 8 ft and the other is 4 ft.  We need to calculate the "opposite side" (that is, the length of the vertical side, the height of the top of the ladder above the ground, using the Pythagorean Theorem, and then subtract the smaller result from the larger.

First triangle:  (opp)^2 + (8 ft)^2 = 16^2

Second triangle:  (opp)^2 + (4 ft)^2 = 16^2

Finish this work.  Determine "opp" in each case.  Subtract the smaller "opp" from the larger "opp."  The difference is the answer to this question.