Arepairman leans the top of an 8 ft ladder against the top of a stone wall the base of the ladder is 5.5 ft from the wall about how tall is the wall round to the nearest tenth of a foot

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!