A plumb bob is a weight hung at the end of a string, called a plumb line. The weight pulls the string down so that the plumb line is perfectly vertical. Suppose that the angle formed by the wall and the roof is 123° and the angle formed by the plumb line and the roof is 123°. How does this show that the wall is perfectly vertical?
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In this scenario, the plumb line is perfectly vertical because it is aligned with the roof at an angle of 123° and also aligned with the wall at an angle of 123°.
When the plumb line is attached to the roof, which forms the angle of 123° with the wall, and it hangs freely, it naturally aligns itself perfectly perpendicular to the roof. This is because a plumb line always hangs vertically due to gravity.
Therefore, since the plumb line is perpendicular to the roof, and the roof is at an angle of 123° to the wall, it indicates that the wall must also be perfectly vertical.
This demonstrates that the wall is vertical because the plumb line, which is perfectly vertical, is aligned with both the roof and the wall.
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In this scenario, the fact that the angle formed by the plumb line and the roof is 123° implies that the plumb line is perpendicular to the roof. A plumb line is designed to hang vertically, so the angle between the plumb line and any other surface should be 90° (perpendicular).
Now, if the angle formed by the wall and the roof is also 123°, it means that the wall is parallel to the roof. Since the plumb line is perpendicular to the roof, and the wall is parallel to the roof, it follows that the wall is perfectly vertical.
In summary, when the angle formed by the plumb line and the roof is the same as the angle formed by the wall and the roof, it indicates that the wall is perfectly vertical.
If you have any further questions or need clarification, feel free to ask!