To find the length of the support AB, we can visualize the situation as a right triangle where:
- One leg of the triangle (the vertical distance between the two parallel bars) is 7 feet.
- The angle between the diagonal and the horizontal parallel bar (the top bar) is 45 degrees.
In a right triangle with an angle of 45 degrees, the lengths of the legs are equal. This means the support AB makes an isosceles right triangle with both legs being the same length.
Given that one leg (the vertical distance) is 7 feet, the horizontal leg (which is also 7 feet at a 45-degree angle) is what we need to use to find the hypotenuse, which is the length of support AB.
Using trigonometric relations, we can find the length of the support AB as follows:
\[ \text{Support AB (hypotenuse)} = \frac{\text{Distance between bars}}{\sin(45^\circ)} = \frac{7 \text{ feet}}{\frac{\sqrt{2}}{2}} = 7 \times \frac{\sqrt{2}}{1} = 7\sqrt{2} \]
However, the specific formula you're looking for to match the provided options and correctly calculate the length of support AB can be determined by using the sine function corresponding to the 45-degree angle.
Therefore, the correct formula corresponding to the given options is:
\[ \text{Support AB} = \frac{7}{\sin(45^\circ)} \]
So the correct answer from the options provided is:
7 divided by sin 45 degrees.
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