We need to find the length of the hypotenuse AC of the given right triangle.
In order to do so, we can use the sine of angle ACB:
[tex]\begin{gathered} \sin\theta=\frac{\text{ opposite leg}}{\text{ hypotenuse}} \\ \\ \text{ hypotenuse }=\frac{\text{ opposite leg}}{\sin\theta} \end{gathered}[/tex]
In this problem, we have:
[tex]\begin{gathered} \theta=65\degree \\ \\ \text{ opposite leg }=12\text{ ft} \\ \\ \text{ hypotenuse }=AC \end{gathered}[/tex]
Thus, AC, in feet, is given by:
[tex]\begin{gathered} AC=\frac{12}{\sin65\degree} \\ \\ AC=12\cosec65\degree \end{gathered}[/tex]
Answer: b) 12 cosec 65°
