To find the distance from the top of the wall portion to the highest part of the triangle peak, we first visualize the roof as a right triangle. The roof is shaped like an isosceles right triangle, where the peak (the highest point) is directly in the center, and the two walls of the house are the legs of the triangle.
Since the distance from either wall to the peak of the triangle is 5 feet, the base of this triangle is 10 feet (5 feet to the left wall and 5 feet to the right wall).
For a right triangle, we can use the Pythagorean theorem to determine the height of the triangle. Given that this is an isosceles right triangle, the two legs (the height and half of the base) are related as follows:
Let:
- Height = h (the distance we are looking for)
- Half of the base = 5 feet (since 5 feet is half of the total 10 feet base)
Since it is a right triangle, we can apply the Pythagorean theorem:
\[ h^2 + (5)^2 = (5\sqrt{2})^2 \]
Where \(5\sqrt{2}\) is the length of the hypotenuse (the slope of the triangle).
To get the height, we recognize that, in a 45°-45°-90° triangle:
- The legs (height and half the base) are equal.
Since one leg (half of the base) = 5 feet, then the height is also equal to the length of the other leg:
Thus:
- Height \( h = 5 \text{ feet} \)
Therefore, the distance from the top of the wall to the peak of the triangle-shaped roof is 5 feet.
Final answer, rounded to the nearest tenth: 5.0 feet.
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