I've added an image for illustrative purposes, where h is the height of the birdcage.
We can see that we'll need to use the pythagorean theorem which, when given the length of the diagonal and one of the perpendicular lengths of the triangle, is:
[tex] {a}^{2} = {c}^{2} - {b}^{2} [/tex]
Substituting the information into this equation:
[tex] {h}^{2} = {15}^{2} - {9}^{2} \\ h = \sqrt{225 - 81} \\ h = \sqrt{144} \\ h = 12 \: cm[/tex]
Therefore, the height of the birdcage is 12cm.
