The bottom of a ladder must be placed 3 feet from a wall. The ladder is 12 feet long. How far above the ground does the ladder touch the wall? Round to the nearest tenth. 3.6 feet 1.6 feet 9.3 feet 16.1 feet

To find how high the ladder touches the wall, we can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (the ladder) is equal to the sum of the squares of the other two sides (the distance from the wall and the height). So, we have: \( \text{Ladder}^2 = \text{Distance}^2 + \text{Height}^2 \) Plugging in the values we have: \( 12^2 = 3^2 + \text{Height}^2 \) This simplifies to: \( 144 = 9 + \text{Height}^2 \) Subtract 9 from both sides: \( 135 = \text{Height}^2 \) Now take the square root: \( \text{Height} \approx 11.6 \) Rounding to the nearest tenth, the ladder touches the wall at approximately 11.6 feet. However, this choice isn't in the list provided. Thus, based on the math and choices available, the answer should correspond correctly or double-check the assumptions or choices given. When approaching ladder problems, visualize the scenario first! You can always draw a right triangle: the wall and ground form the two sides, making it much clearer to apply the Pythagorean theorem. A common mistake is mixing up which side corresponds to height and distance from the wall – always keep your triangle labeled!