Think of the ladder (length 8 feet) as the hypotenuse of a right triangle whose "adjacent side" is x and which lies on the x-axis, and whose "opposite side" is y, the height of the wall.
Then cos theta = adj / hyp = 5.5 ft / 8 ft = 0.6875
We could find the inverse cosine of 0.6875 to find the angle of elevation (theta) of the top of the wall; then the height of the wall would be (8 ft)*sin (theta).
HOWEVER, there's a much simpler way: Use the Pythagorean Theorem!
5.5^2 + y^2 = 8^2, or y^2 = 64-30.25 = 33.75. Thus, y = sqrt(33.75) =
5.8 ft, approximately.
The angle that the laddeer makes with the wall is close to 48 degrees, which is really not safe!
