The bottom of a ladder must be placed 4 feet from a wall. The ladder is 12 feet long. How far above the ground does the ladder touch the wall? Round your answer to the nearest tenth. Answer:

To find the height at which the ladder touches the wall, we can use the Pythagorean theorem. The distance from the wall to the bottom of the ladder (4 feet) and the height (let's call it \( h \)) form a right triangle with the ladder serving as the hypotenuse. Using the equation \( a^2 + b^2 = c^2 \), we have: \[ 4^2 + h^2 = 12^2 \] \[ 16 + h^2 = 144 \] \[ h^2 = 128 \] \[ h = \sqrt{128} \approx 11.3 \text{ feet} \] So the ladder touches the wall at approximately 11.3 feet above the ground. Now, rounding that answer to the nearest tenth gives us **11.3 feet**.