Question

david wants to find the height of a building. He places his 71 feet ladder against the very top of the building. David then measures the base of the building to his ladder which is 11 feet. How tall is the building? Round your answer to the nearest tenth. Click Here for Help Video.

Answer 1

To find the height of the building, we can use the Pythagorean theorem. In this case, we have a right triangle formed by the height of the building (let's call it \( h \)), the distance from the base of the building to the bottom of the ladder (11 feet), and the length of the ladder (71 feet).

According to the Pythagorean theorem:

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

where:
- \( a \) is the height of the building (\( h \)),
- \( b \) is the distance from the base of the building to the bottom of the ladder (11 feet),
- \( c \) is the length of the ladder (71 feet).

Thus, we can set it up as:

\[
h^2 + 11^2 = 71^2
\]

Calculating \( 11^2 \) and \( 71^2 \):

\[
11^2 = 121
\]
\[
71^2 = 5041
\]

Now we can rewrite the equation:

\[
h^2 + 121 = 5041
\]

Subtract 121 from both sides:

\[
h^2 = 5041 - 121
\]
\[
h^2 = 4920
\]

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

\[
h = \sqrt{4920}
\]

Calculating the square root of 4920:

\[
h \approx 70.2 \text{ feet}
\]

Rounding to the nearest tenth, the height of the building is approximately:

\[
\boxed{70.2 \text{ feet}}
\]