To find the distance from the top of the wall portion to the highest part of the triangle peak, we can visualize the triangular roof.
Since the base distance (the distance from either wall to the peak) is 5 feet on each side, the total base of the triangle is:
\[ 5 \text{ feet} + 5 \text{ feet} = 10 \text{ feet} \]
The triangle shape formed by the roof is a right triangle, with the peak at the top (the apex) and the two slanted sides meeting at that point.
When we look at the triangle vertically, we can drop a perpendicular (height) from the peak to the base. This perpendicular line will bisect the base of the triangle since the roof is symmetrical.
Thus, the half base length (from the midpoint to either end, which is where the walls meet) is:
\[ \frac{10 \text{ feet}}{2} = 5 \text{ feet} \]
Let \(h\) be the height of the triangle. Using the properties of a right triangle, we have:
- Half the base = 5 feet (adjacent side)
- Height = \(h\) (opposite side)
Since we have a symmetrical right triangle that has no given angle or direct distance from the wall, we need to rely on the idea that height \(h\) extends directly upward from the base (the top of the side walls) to the peak.
Based on the question's details, it sounds as though only the width of 5 feet to the peak is necessary to calculate. The height is typically independent, as the peak can be at any height, but in symmetrical structures, the peak can be calculated directly.
The exact height would be related to how high Sarah wants her triangle to be. Without specific instructions on the height or angle, standard setups typically expect equal triangular dimensions—so we assume 5 feet equals height \(h\) unless specified otherwise.
Thus, the final distance from the top of the wall to the triangle peak is:
\[ \boxed{5.0} \text{ feet} \]
This gives us the total height of the roof peak as asked.
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