The question describes a right triangle with hypotenuse as 9 and one of the angles as 75 degrees. We are looking for the length of the leg adjacent the given angle 75 degrees.
Recall that:
[tex] \cos{\theta}=\cfrac{adj}{hyp}\\ \\ \Rightarrow\cos75^o=\cfrac{x}{9}\\ \\ \Rightarrow x=9\cos75^o=9(0.2588)=2.3 ft. [/tex]
