a repairman leans the top of a 9ft ladder against the top of a stone wall. the base of the ladder is 5.5ft from the wall. about how tall is the wall? round to the nearest tenth of a foot.

Using the Pythagorean theorem:

a^2 + b^2 = c^2

a and b are the sides and c is the hypotenuse.

The length of the ladder would be the hypotenuse and the base away from the wall would be one side.

So now we have:

5.5^2 + b^2 = 9^2

Simplify:

30.25 + b^2 = 81

Subtract 30.25 from each side:

b^2 = 81 - 30.25

b^2 = 50.75

Take the square root of both sides:

b = √50.75

b = 7.123

Rounded to the nearest tenth of a foot = 7.1 feet.