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
