Look at the rectangle. The bottom side measures 8 miles, so the top side also measures 8 miles.
Now look at the upper right triangle. For the angle of 32 deg, the top side of the triangle is the adjacent leg of the triangle. The air distance, marked x, is the hypotenuse of the triangle.
The trig ratio that relates the adjacent leg and the hypotenuse is the cosine.
[tex] \cos \theta = \dfrac{adj}{hyp} [/tex]
[tex] \cos 32^\circ = \dfrac{8~miles}{x} [/tex]
[tex] x = \dfrac{8~miles}{\cos 32^\circ} [/tex]
[tex] x = 9.4 ~miles [/tex]
