Observe that the triangle has a square angle.
So the triangle is a right angled triangle, and hence the Pythagoras Theorem is applicable.
[tex]\text{Base}^2+Height^2=Hypotenuse^2[/tex]
Substitute the values,
[tex]12^2+Height^2=15^2\Rightarrow Height^2=225+144\Rightarrow Height=9[/tex]
Thus, the height i.e. length of the wall support is 9 inches.
