Answer:
[tex]\sqrt{55}[/tex]
Step-by-step explanation:
Based off of what we do know, if we can find length DB we can use the pythagorous theorem (I will be assigning the variable z)
[tex]x^{2} =36+z^{2} \\\\y^{2}=25+z^2\\\\x^{2} +y^2=121\\\\[/tex]
First equation is for triangle ABD
Second is for BCD
And the last one is for ACD
Substitute [tex]x^{2}[/tex] and [tex]y^2[/tex]
[tex]36+z^2+25+z^2=121\\\\61+2z^2=121\\\\2z^2=60\\\\z^2=30\\\\z=\sqrt{30}[/tex]
As discovered before
[tex]y^2=25+z^2\\\\y^2=25+30\\\\y^2=55\\\\y=\sqrt{55}[/tex]
