Question

A ladder that is 22 feet long is leaning against a 15-foot tall wall. Label the photo with the correct side lengths based on the given information. *Note, you will have to solve for the missing side. (3 points) Drop target 1 Drop target 2 Drop target 3 Skip to navigation

Answer 1

To solve for the missing side in this scenario, we can use the Pythagorean theorem, which states that in a right triangle:

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

where:
- \( c \) is the length of the hypotenuse (the longest side),
- \( a \) and \( b \) are the lengths of the other two sides.

In this case:
- The length of the ladder (hypotenuse) \( c = 22 \) feet,
- The height of the wall \( a = 15 \) feet,
- We need to find the length of the base (the distance from the wall to the bottom of the ladder), which we'll call \( b \).

First, we rearrange the Pythagorean theorem to solve for \( b \):

\[ b = \sqrt{c^2 - a^2} \]

Now we can plug in the values:

1. Calculate \( c^2 \):
\[ c^2 = 22^2 = 484 \]

2. Calculate \( a^2 \):
\[ a^2 = 15^2 = 225 \]

3. Substitute these values into the equation for \( b \):
\[ b = \sqrt{484 - 225} \]
\[ b = \sqrt{259} \]
\[ b \approx 16.12 \text{ feet} \]

Now we have:
- The height of the wall (15 feet),
- The length of the ladder (22 feet),
- The distance from the wall to the bottom of the ladder (approximately 16.12 feet).

### Labeling the Diagram:
In the diagram, label:
- The hypotenuse as "Ladder: 22 feet",
- The vertical side (height of the wall) as "Wall Height: 15 feet",
- The horizontal side (distance from the wall) as "Base: 16.12 feet".

This clearly shows the side lengths you have based on the given information!