To find the distance from the top of the wall to the highest part of the triangle peak, we will analyze the triangle-shaped roof Sarah designed.
Given the roof is a right triangle with a 90° angle at the peak and is symmetrical, we can determine the following:
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The distance from either wall to the peak is 5 feet, which represents the base of the triangle. Since the roof is symmetrical, the entire base of the triangle is 10 feet (5 feet on each side).
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In a right triangle, we can consider half of this base to find the height. So, the half of the base (width of one side) is: \[ \text{Base} = 5 \text{ feet} \] This half-base will be the adjacent side of the right triangle when we visualize it.
Let \( h \) be the height of the triangle from the top of the wall to the peak.
Now, we have a right triangle where:
- The base (half) is 5 feet,
- The height is \( h \),
- And the hypotenuse is the slanted side of the roof.
Since no angles or information about the slanted side has been provided, we will simply need to set \( h \) equal to the base height of the peak triangle, which is usually equal for a symmetric triangle.
Since we need to determine the answer from the wall's apex height to the roof's peak directly related to its symmetrical height as a right triangle, we consider the right-angle property, thus we know: Assuming \( h = 5 \text{ feet} \) forms a right isosceles triangle.
Therefore, the height from the top of the wall to the triangle peak is:
\[ h = 5 \text{ feet} \]
Thus, the height from the top of the wall to the highest part of the triangle peak is:
\[ \boxed{5.0} \text{ feet} \]
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