Question

David wants to find the height of a building. He places his 44 feet ladder against the very top of the building. David then measures the base of the building to his ladder which is 10 feet. How tall is the building? Round your answer to the nearest tenth.

a2+b2=c2

Answer 1

To find the height of the building, we can use the Pythagorean theorem, which states that in a right triangle:

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

Here:
- \( a \) is the height of the building (which we are trying to find),
- \( b \) is the distance from the base of the building to the bottom of the ladder (which is 10 feet),
- \( c \) is the length of the ladder (which is 44 feet).

We can rearrange the Pythagorean theorem to solve for \( a \):

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

Substituting the known values:

\[
a^2 = 44^2 - 10^2
\]

Calculating \( 44^2 \) and \( 10^2 \):

\[
44^2 = 1936
\]
\[
10^2 = 100
\]

Now, substituting these values back into the equation:

\[
a^2 = 1936 - 100 = 1836
\]

Next, we take the square root of 1836 to find \( a \):

\[
a = \sqrt{1836} \approx 42.9
\]

Therefore, the height of the building is approximately **42.9 feet** when rounded to the nearest tenth.