To find the height of the building, we can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (the ladder in this case) is equal to the sum of the squares of the other two sides (the height of the building and the distance from the base of the building to the base of the ladder).
Let:
- \( h \) = height of the building,
- \( d \) = distance from the base of the building to the base of the ladder (111111 feet),
- \( L \) = length of the ladder (717171 feet).
According to the Pythagorean theorem: \[ L^2 = h^2 + d^2 \]
Substituting the given values: \[ 717171^2 = h^2 + 111111^2 \]
Calculating \( 717171^2 \) and \( 111111^2 \): \[ 717171^2 = 514,464,726,241 \] \[ 111111^2 = 12,345,432,321 \]
Now, substituting these values back into the equation: \[ 514464726241 = h^2 + 1234543221 \]
Now, isolate \( h^2 \): \[ h^2 = 514464726241 - 1234543221 \] \[ h^2 = 513230183020 \]
Now, take the square root of both sides to find \( h \): \[ h = \sqrt{513230183020} \approx 716049.4 \]
Rounding to the nearest tenth, the height of the building is approximately: \[ \boxed{716049.4} \text{ feet} \]