Fast a 10 ft. ladder is resting against the wall. the ladder touches the ground 6 ft. away from the wall. what angle, rounded to the nearest tenth, is the bottom of the ladder making with the ground?

Think of the right triangle formed by the ladder, the height of the upper end of the ladder and the distance of the bottom of the ladder from the wall.

Then x = 6 ft and the hyp is 10 ft.  The trig function cos theta  equals "adj side" / hyp, so, in this case,

cos theta = 6/10 = 0.6.  Use the arccos x function on your calculator to find the angle x:

x = 0.927 (radians) = 53.1 degrees.