Y= 17.23
By Pythagoras theorem.
[tex] {x}^{2} + {y}^{2} = {z}^{2} [/tex]
in the figure , we can see in ∆ABC
[tex] {x}^{2} + {y}^{2} = 25 + 8[/tex]
_______eq.(I)
In ∆BCD,
[tex] {y}^{2} = {z}^{2} + {25}^{2} [/tex]
_______eq.(ii)
In ∆ABD
[tex] {x}^{2} = {z}^{2} + {8}^{2} [/tex]
____eq.(iii)
substitute eq.(iii) in eq.(i)
we get,
[tex] {z}^{2} + 64 + {y}^{2} = 33[/tex]
from eq.(ii)
[tex] {z}^{2} = {y}^{2} - 625[/tex]
substitute this to above equation...
we get,
[tex] {y}^{2} - 625 + {y}^{2} + 64 = 33[/tex]
2y^2 = 33+625-64
y^2= 594/2
[tex]y = \sqrt{297} [/tex]
Hence , y= 17.23
