Question

David wants to find the height of a building. He places his 323232 feet ladder against the very top of the building. David then measures the base of the building to his ladder which is 131313 feet. How tall is the building? Round your answer to the nearest tenth.

Answer 1

To find the height of the building, we can use the Pythagorean theorem. The ladder, the height of the building, and the distance from the base of the building to the foot of the ladder form a right triangle. In this scenario:

- Let \( h \) be the height of the building (the vertical side of the triangle).
- The length of the ladder is the hypotenuse, which is 32 feet.
- The distance from the base of the building to the foot of the ladder is 13 feet.

According to the Pythagorean theorem, we have:

\[
a^2 + b^2 = c^2
\]

where:
- \( a \) is the height of the building (\( h \)),
- \( b \) is the distance from the base of the building to the foot of the ladder (13 feet),
- \( c \) is the length of the ladder (32 feet).

Substituting the values into the equation:

\[
h^2 + 13^2 = 32^2
\]

Calculating \( 13^2 \) and \( 32^2 \):

\[
h^2 + 169 = 1024
\]

Now, we can isolate \( h^2 \):

\[
h^2 = 1024 - 169
\]
\[
h^2 = 855
\]

Next, we take the square root of both sides to find \( h \):

\[
h = \sqrt{855} \approx 29.2
\]

Thus, rounding to the nearest tenth, the height of the building is

\[
\boxed{29.2} \text{ feet.}
\]