To find the height of the building, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the ladder, in this case) is equal to the sum of the squares of the lengths of the other two sides (the height of the building and the distance from the base of the building to the foot of the ladder).
Let:
- \( h \) = height of the building
- \( d \) = distance from the base of the building to the foot of the ladder = 10 feet
- \( l \) = length of the ladder = 44 feet
According to the Pythagorean theorem: \[ l^2 = h^2 + d^2 \]
Substituting the values: \[ 44^2 = h^2 + 10^2 \]
Calculating the squares: \[ 1936 = h^2 + 100 \]
Now, subtract 100 from both sides: \[ 1936 - 100 = h^2 \] \[ 1836 = h^2 \]
Now, take the square root of both sides to find \( h \): \[ h = \sqrt{1836} \approx 42.9 \text{ feet} \]
Rounding to the nearest tenth, the height of the building is approximately \( 42.9 \) feet.