A 12-foot ladder is placed against a vertical wall of a building, with the bottom of the ladder standing on the level ground 7 feet from the base of the building. How high up the wall does the ladder reach? (Round to the nearest hundredth as needed.)

the ladder reaches up to 9.75 ft. high

Step-by-step explanation:

a^2+b^2=c^2

plug in the numbers

a^2+49=144

then subtract 49 from 144

a^2=95

then sq 95

a=9.75

Answer: the height that the ladder reaches is 4 feet.

Step-by-step explanation:

The ladder forms a right angle triangle with the building and the ground. The length of the ladder represents the hypotenuse of the right angle triangle. The height, h from the top of the ladder to the base of the building represents the opposite side of the right angle triangle.

The distance from the bottom of the ladder to the base of the building represents the adjacent side of the right angle triangle.

To determine the height that the ladder reaches, h, we would apply Pythagoras theorem which is expressed as

Hypotenuse² = opposite side² + adjacent side²

12² = 7² + h²

144 = 49 + h²

h² = 144 - 49

h² = 95

h = √95

h = 7.45 feet