Joshua has a ladder that is 12 ft long. he will lean the ladder against a vertical wall. for safety reasons, he wants the angle the ladder makes with the ground to be no greater than 75°. is it possible for joshua to lean the ladder against the wall so that the top of the ladder is at least 11.8 ft above the ground?

We first determine the height that the top of the ladder will reach given that the angle to be made is no greater than 75°. In the right triangle formed, the hypotenuse is 12. The trigonometric function that is derived from the scenario is,
                                     x = (sin 75°)(12 ft) = 11.59 ft
Thus, the highest point that the ladder will reach should only be approximately equal to 11.59 ft.