Question

David wants to find the height of a building. He placed his 80 feet ladder against the very top of the building. David then measure the base of the building to his ladder which is 7 feet. How tall is the building? Round your answer to the nearest tenth.

H =

Answer 1

To find the height of the building, we can use the Pythagorean theorem. In this scenario, 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's denote:
- \( H \) as the height of the building,
- \( L \) as the length of the ladder (80 feet),
- \( D \) as the distance from the base of the building to the bottom of the ladder (7 feet).

According to the Pythagorean theorem:

\[
L^2 = H^2 + D^2
\]

We can rearrange the equation to solve for \( H \):

\[
H^2 = L^2 - D^2
\]

Substituting in the values:

- \( L = 80 \) feet,
- \( D = 7 \) feet.

Calculating \( L^2 \) and \( D^2 \):

\[
L^2 = 80^2 = 6400
\]

\[
D^2 = 7^2 = 49
\]

Now, substituting back into the equation:

\[
H^2 = 6400 - 49 = 6351
\]

Taking the square root of both sides to find \( H \):

\[
H = \sqrt{6351} \approx 79.8
\]

Therefore, the height of the building is approximately:

\[
\boxed{79.8} \text{ feet}
\]