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:
-
Calculate \( c^2 \): \[ c^2 = 22^2 = 484 \]
-
Calculate \( a^2 \): \[ a^2 = 15^2 = 225 \]
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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!