Question
- In an A-frame house, the two congruent sides extend from the ground to form a
angle at the peak. What angle does each side form with the ground?
?
78
.
Ask by Montgomery Weston. in the United States
Jan 21,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
Each side forms a
angle with the ground.
Solution
To determine the angle each side of the A-frame house forms with the ground, let’s analyze the situation step by step.
-
Understanding the Structure:
- The A-frame house forms an isosceles triangle where the two congruent sides meet at the peak.
- The apex angle at the peak is
.
-
Calculating the Base Angles:
- The sum of all angles in a triangle is
. - Let each base angle be
. - Therefore:
- The sum of all angles in a triangle is
-
Conclusion:
- Each side of the A-frame forms a
angle with the ground.
- Each side of the A-frame forms a
Answer:
Answered by UpStudy AI and reviewed by a Professional Tutor
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Beyond the Answer
To find the angle each side forms with the ground, we need to understand the structure of the A-frame house. The two congruent sides create a peak angle of
. Since the peak is at the top of the triangle formed by the sides, each of the two base angles at the ground must share the remainder of the
that is available in a triangle.
So, we subtract
from
, which gives us
. However, since there are two angles at the base, we divide that result by 2, yielding
. Therefore, each side forms a
angle with the ground.
Now, for fun: Did you know that the shape of A-frame houses isn’t just aesthetically pleasing? Their design is particularly great for snow areas as the steep slant allows snow to slide off easily, minimizing the risk of accumulation that could lead to structural issues. So, whether you’re a fan of skiing or simply love cozy cabins, the A-frame’s design has your back (and roof)!