To find the height of the building, we can use the Pythagorean theorem, which states:
\[ a^2 + b^2 = c^2 \]
where:
- \( a \) is the height of the building (which we need to find),
- \( b \) is the distance from the base of the building to the bottom of the ladder (10 feet),
- \( c \) is the length of the ladder (44 feet).
Plugging in the values we have:
\[ a^2 + 10^2 = 44^2 \]
This simplifies to:
\[ a^2 + 100 = 1936 \]
Now, subtract 100 from both sides:
\[ a^2 = 1936 - 100 \] \[ a^2 = 1836 \]
Next, we take the square root of both sides to find \( a \):
\[ a = \sqrt{1836} \]
Calculating the square root:
\[ a \approx 42.9 \]
So, the height of the building is approximately 42.9 feet (rounded to the nearest tenth).