To find the height of the building, we can use the Pythagorean theorem, which relates the lengths of the sides of a right triangle. The ladder, the height of the building, and the distance from the base of the building to the bottom of the ladder form a right triangle.
Let:
- \( h \) be the height of the building,
- The length of the ladder is 34 feet (the hypotenuse),
- The distance from the base of the building to the ladder is 9 feet (one leg of the triangle).
According to the Pythagorean theorem:
\[ a^2 + b^2 = c^2 \]
In our case:
- \( a = h \) (height of the building),
- \( b = 9 \) feet (distance from the base to the ladder),
- \( c = 34 \) feet (length of the ladder).
Substituting these values into the equation:
\[ h^2 + 9^2 = 34^2 \]
Calculate \( 9^2 \) and \( 34^2 \):
\[ h^2 + 81 = 1156 \]
Now, subtract 81 from both sides:
\[ h^2 = 1156 - 81 \]
\[ h^2 = 1075 \]
Next, take the square root of both sides to find \( h \):
\[ h = \sqrt{1075} \]
Calculating \( \sqrt{1075} \):
\[ h \approx 32.8 \]
Therefore, the height of the building is approximately 32.8 feet when rounded to the nearest tenth.
So, the final answer is:
\[ h \approx 32.8 \text{ feet} \]