A 23ft ladder is placed against a vertical wall of a​ building, with the bottom of the ladder standing on level ground 16ft from the base of the building. how high up the wall does the ladder​ reach? the ladder reaches nothing feet up the wall. ​(round to the nearest​ hundredth.)

The orientation of the ladder with the wall forms a right triangle. The ladder length is the hypotenuse of the triangle, the distance between the ladder at ground level and the base of the wall is the horizontal leg of the triangle, the height of the ladder is the vertical leg of the triangle.

Since we have a right triangle, we can use the Pythagorean theorem.

Let x = the height of the ladder


Write the equation for the Pythagorean theorem using the information.

x2 + 162 = 232


Solving for x, we have

x2 = 232 - 162

x = √(232 - 162)

x = √(529 - 256)

x = √(273)

x = 16.52


The ladder reaches 16.52 feet high.