In a A-frame house, the two congruent sides extend from the ground to form a 34 degree angle at the peak. What angle does each side form with the ground ?
(180-34)/2 = 73
To determine the angle that each side forms with the ground in an A-frame house, we can start by visualizing the situation.
Let's consider an A-frame house where the two congruent sides meet at the peak, forming a 34-degree angle. Since the sides are congruent, the two angles formed with the ground will also be congruent.
To find this angle, we can use the fact that the sum of the angles in a triangle is 180 degrees. In this case, the triangle consists of the two congruent sides and the ground. Thus, the sum of the three angles in the triangle is 180 degrees.
Let's denote the angle formed between each side and the ground as "x." Since the two congruent sides are forming a 34-degree angle at the peak, the remaining angle of the triangle, formed between the two congruent sides, is also 180 - 34 = 146 degrees.
Since the two congruent sides form a straight line, their sum should be 180 degrees. So, we have the equation:
x + x + 146 = 180
Combining like terms, we get:
2x + 146 = 180
Next, we can isolate 2x by subtracting 146 from both sides of the equation:
2x = 180 - 146
2x = 34
Finally, dividing both sides by 2:
x = 34 / 2
x = 17
Therefore, each side forms a 17-degree angle with the ground in an A-frame house.
To determine the angle that each side forms with the ground in an A-frame house, we need to consider the fact that an isosceles triangle is formed by the two congruent sides and the ground. In an isosceles triangle, the base angles, or the angles formed by the congruent sides and the base, are equal.
Since the peak angle in the A-frame house is 34 degrees, each base angle is half of the peak angle.
Thus, each side forms an angle of 34 degrees divided by 2, which is equal to 17 degrees, with the ground.