Sure, let's find the height [tex]\( h \)[/tex] of the wall using the properties of a [tex]\( 45^{\circ}-45^{\circ}-90^{\circ} \)[/tex] triangle.
A [tex]\( 45^{\circ}-45^{\circ}-90^{\circ} \)[/tex] triangle is a special type of right triangle where the two legs are equal in length, and the hypotenuse is [tex]\( \sqrt{2} \)[/tex] times the length of each leg.
Given:
- One of the legs of the triangle (which we'll call [tex]\( a \)[/tex]) is [tex]\( 6.5 \)[/tex] feet.
We need to find the height [tex]\( h \)[/tex], which corresponds to the hypotenuse of the triangle.
According to the properties of a [tex]\( 45^{\circ}-45^{\circ}-90^{\circ} \)[/tex] triangle:
[tex]\[
h = a \sqrt{2}
\][/tex]
Substitute [tex]\( a = 6.5 \)[/tex] feet into the equation:
[tex]\[
h = 6.5 \times \sqrt{2}
\][/tex]
By multiplying these values together, we get:
[tex]\[
h \approx 9.19238815542512
\][/tex]
Therefore, the height of the wall, [tex]\( h \)[/tex], is approximately [tex]\( 9.19238815542512 \)[/tex] feet.
