Sarah is building a dog house. She has created the rectangular house and just needs to build the roof to fit. She designs a triangle-shaped roof by using two sheets of wood, forming a 90° angle at the peak. Looking at the front of the dog house, the distance from either wall is 5 feet across. If the triangle portion is symmetrical, what is the distance from the top of the wall portion to the highest part of the triangle peak? Round your answer to the nearest tenth.(1 point)

Question

feet

Answer 1

To find the distance from the top of the wall to the highest part of the triangle peak, we can visualize the situation as follows:

1. The base of the triangle (the width of the dog house) is 5 feet across from one wall to the other.
2. Since the triangle is symmetrical, the peak lies directly in the center of the base. Therefore, the base of the triangle is 5 feet wide, which means each side of the triangle (from the peak to the wall) is 2.5 feet (half of 5 feet).
3. The peak forms a right triangle with half of the base and the height from the wall to the peak.

Since it's a right triangle, we can apply the Pythagorean theorem if we want to find the height (h) when we have the base (b) and the hypotenuse (the slant height, which we don't have but need only the height):

However, since the information provided does not include the slant height or any inclination angle, it directly asks for the distance to the peak above the wall and assumes that it is a vertical line.

In this case, the height of the triangle (from the highest point to the walls where the base of the triangle meets the walls) is 5 feet directly above the peak.

Thus, the distance from the top of the wall portion to the highest part of the triangle peak is:

5 feet (rounded to the nearest tenth)

Answer 2

5 is wrong