Answer:
[tex]h = 8\sqrt{2}[/tex]
Step-by-step explanation:
[tex]h^{2} + 4^{2} = a^{2} \\h^{2} + 32^{2} = b^{2} \\a^{2} + b^{2} = 36^{2}[/tex]
Add the top 2 equations
[tex]\\h^{2} + 4^{2} + h^{2} + 32^{2} = a^{2} + b^{2} = 36^{2}[/tex]
[tex]2h^{2} + 16 + 1024 = 1296\\2h^{2} + 1040 = 1296\\2h^{2} = 256\\h^{2} =128\\h = \sqrt{128} = 8\sqrt{2}[/tex]
