Answer:
a = 6 in
Step-by-step explanation:
Using Pythagoras' Theorem [tex]a^2+b^2=c^2[/tex], where a and b are the legs, and c is the hypotenuse of a right triangle.
[tex]a^2+b^2=9^2[/tex]
[tex]5^2+DC^2=b^2[/tex]
[tex]4^2+DC^2=a^2[/tex]
[tex]\implies 4^2+DC^2+5^2+DC^2=9^2[/tex]
[tex]\implies 2 \ DC^2 =40[/tex]
[tex]\implies DC^2=20[/tex]
If [tex]a^2=4^2+DC^2=16+20=36[/tex]
[tex]\implies a=\sqrt{36} =6[/tex]
