To find the height of the wall, we need to consider the properties of a 45-45-90 triangle. In a 45-45-90 triangle, the lengths of the legs are equal, and the length of the hypotenuse is the leg length multiplied by [tex]\(\sqrt{2}\)[/tex].
Given:
- One leg of the 45-45-90 triangle is 6.5 feet.
1. According to the properties of the 45-45-90 triangle, the length of the hypotenuse can be calculated using the formula:
[tex]\[
\text{Hypotenuse} = \text{Leg Length} \times \sqrt{2}
\][/tex]
2. Substituting the given leg length (6.5 feet) into the formula:
[tex]\[
\text{Hypotenuse} = 6.5 \times \sqrt{2}
\][/tex]
3. Now, calculating the value:
[tex]\[
6.5 \times \sqrt{2} \approx 6.5 \times 1.41421356237 \approx 9.19238815542512 \, \text{feet}
\][/tex]
Therefore, the height [tex]\(h\)[/tex] of the wall is approximately:
[tex]\[
9.19238815542512 \, \text{feet}
\][/tex]
This is the height (hypotenuse in this context) we needed to find.
