Given the picture that shows a barn door, you can identify that a Right Triangle is formed (look at the picture below):
Notice that the Right Triangle is ABC.
You need to use the following Trigonometric Function, in order to find the length of the support AB (notice that this is the hypotenuse of the Right Triangle) :
[tex]sin\theta=\frac{opposite}{hypotenuse}[/tex]
In this case:
[tex]\begin{gathered} \theta=45° \\ opposite=7 \\ hypotenuse=AB \end{gathered}[/tex]
Then, you can substitute values and solve for AB:
[tex]sin45\text{\degree}=\frac{7}{AB}[/tex][tex]AB\cdot sin45\text{\degree}=7[/tex][tex]AB=\frac{7}{sin45°}[/tex]
Hence, the answer is: Third option.
