Question

A 14​-foot ladder is leaning against a​ building, with the base of the ladder 5 feet from the building. How high up on the building will the top of the ladder​ reach?
Question content area bottom
Part 1
The ladder will reach
  
enter your response here ft high up on the building.
​(Round to the nearest​ tenth.)

Answer 1

To find out how high the top of the ladder reaches on the building, we can use the Pythagorean theorem. The ladder forms a right triangle where:

- The length of the ladder is the hypotenuse (\(c\)).
- The distance from the base of the ladder to the building is one leg (\(a\)).
- The height that the ladder reaches on the building is the other leg (\(b\)).

Given:
- \(c = 14\) feet (the length of the ladder)
- \(a = 5\) feet (the distance from the base of the ladder to the building)

We need to find \(b\) (the height up the building). According to the Pythagorean theorem:

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

Plugging in the values:

\[
14^2 = 5^2 + b^2
\]

Calculating the squares:

\[
196 = 25 + b^2
\]

Now, isolate \(b^2\):

\[
b^2 = 196 - 25
\]
\[
b^2 = 171
\]

Now take the square root to find \(b\):

\[
b = \sqrt{171} \approx 13.038
\]

Rounding to the nearest tenth:

\[
b \approx 13.0 \text{ feet}
\]

Thus, the ladder will reach approximately **13.0 feet** high up on the building.