We have a 45-45-90 triangle with hypotenuse
[tex]24 \sqrt{6} \: \: \: leg \: x \: therefore \: has \: length \\ \frac{24 \sqrt{6} }{ \sqrt{2 \:} \: } \: = \: \frac{24 \sqrt{3} \sqrt{2} }{ \sqrt{2} \: } = 24 \sqrt{3} = x \\ \\ [/tex]
We now work with the 30-60-90. triangle having a side opposite the 60 degree angle of length
[tex]24 \sqrt{3} [/tex]
y, the side opposite the 30 degee angle then has length
[tex] \frac{24 \sqrt{3} }{ \sqrt{3}} = 24[/tex]
The hypotenuse has length twice the side opposite the 30 degree angle = 2y = 48 = z
