In this problem, we are dealing with an isosceles triangle formed by the two congruent sides of an A-frame house. Let's break down the solution step-by-step:
1. Understanding the Triangle:
- We have an isosceles triangle where the two congruent sides form an angle of 34° at the peak (the top vertex of the triangle).
2. Sum of Angles in a Triangle:
- The sum of all internal angles in any triangle is 180°.
3. Identifying the Known Angle:
- The angle at the peak of the triangle is given as 34°.
4. Calculating the Base Angles:
- Since the triangle is isosceles, the two angles at the base (i.e., where the sides meet the ground) are congruent.
- Let each of these base angles be represented as [tex]\( x \)[/tex].
5. Forming an Equation:
- We use the fact that the sum of the angles in a triangle is 180°:
[tex]\[
x + x + 34° = 180°
\][/tex]
- Simplifying this equation:
[tex]\[
2x + 34° = 180°
\][/tex]
6. Solving for [tex]\( x \)[/tex]:
- Subtract 34° from both sides of the equation:
[tex]\[
2x = 180° - 34°
\][/tex]
- This simplifies to:
[tex]\[
2x = 146°
\][/tex]
7. Divide Both Sides by 2:
- To find [tex]\( x \)[/tex], divide 146° by 2:
[tex]\[
x = \frac{146°}{2}
\][/tex]
- Thus, [tex]\( x = 73° \)[/tex].
Therefore, each side of the A-frame house forms a 73° angle with the ground. The angles are [tex]\( 34° \)[/tex] at the peak and [tex]\( 73° \)[/tex] at each base with the ground.
