A 19-f ladder is leaning against a wall and the wall is perpendicular to the ground. The base of the ladder is 8 ft from the wall. How high above the ground is the top of the ladder? The ladder reaches (Simplify your answer. Type an exact answer, using radicals as needed.)

To find how high the ladder reaches on the wall, we can use the Pythagorean theorem. The ladder, the wall, and the ground create a right triangle where the ladder is the hypotenuse. We have: \( c^2 = a^2 + b^2 \) Here, \( c = 19 \) ft (length of the ladder), \( b = 8 \) ft (distance from the wall), and we need to find \( a \) (height up the wall). Plugging in the values: \( 19^2 = a^2 + 8^2 \) \( 361 = a^2 + 64 \) \( a^2 = 361 - 64 \) \( a^2 = 297 \) Now taking the square root: \( a = \sqrt{297} \) So the ladder reaches \( \sqrt{297} \) ft up the wall, which simplifies to \( 3\sqrt{33} \) ft. The ladder reaches \( 3\sqrt{33} \) ft above the ground.