A 38-foot ladder leaning against a wall makes a 70^o angle with the ground. How high up the wall does the ladder reach? (Round your answer to the nearest tenth.)

We can use trigonometry to solve this problem. We know that the ladder, the wall, and the ground form a right triangle, where the ladder is the hypotenuse, the wall is one leg, and the distance from the base of the ladder to the wall (the height we are looking for) is the other leg. Using the given angle and the trigonometric function sine (which relates the opposite side to the hypotenuse), we can set up the following equation: sin(70°) = height of the wall / length of the ladder Rearranging for the height of the wall, we get: height of the wall = sin(70°) x length of the ladder Plugging in the given values, we get: height of the wall = sin(70°) x 38 feet Using a calculator, we find that sin(70°) is \approx imately 0.9397. Multiplying this by 38 feet, we get: height of the wall ? 35.687 feet Rounding this to the nearest tenth, we get that the ladder reaches a height of \approx imately 35.7 feet up the wall.