Question

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. \boxed{} feet

Explanation:

Step1: Identify the right triangle

The ladder, wall, and ground form a right triangle. Let \( a = 3 \) (distance from wall), \( c = 12 \) (ladder length, hypotenuse), and \( b \) be the height on the wall. Use Pythagorean theorem: \( a^2 + b^2 = c^2 \).

Step2: Solve for \( b \)

Rearrange the formula: \( b^2 = c^2 - a^2 \). Substitute values: \( b^2 = 12^2 - 3^2 = 144 - 9 = 135 \). Then \( b = \sqrt{135} \).

Step3: Calculate and round

\( \sqrt{135} \approx 11.6 \) (rounded to nearest tenth).

Answer:

11.6