Answer:
The distance between the centers of the gears is 27.4 inches
Step-by-step explanation:
see the attached figure with letters to better understand the problem
In the right triangle ABC
Applying the Pythagorean Theorem
[tex]AC^2=AB^2+BC^2[/tex]
we have
[tex]BC=CE-EB=9.3-2.4=6.9\ in[/tex]
[tex]AB=DE=26.5\ in[/tex]
substitute
[tex]AC^2=26.5^2+6.9^2[/tex]
[tex]AC^2=749.86\\AC=27.4\ in[/tex]
therefore
The distance between the centers of the gears is 27.4 inches
