Question

Find the value of y.

Answer 1

Answer:

$\sqrt{55}$

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)

$x^{2} =36+z^{2} \\\\y^{2}=25+z^2\\\\x^{2} +y^2=121$

First equation is for triangle ABD

Second is for BCD

And the last one is for ACD

Substitute $x^{2}$ and $y^2$

$36+z^2+25+z^2=121\\\\61+2z^2=121\\\\2z^2=60\\\\z^2=30\\\\z=\sqrt{30}$

As discovered before

$y^2=25+z^2\\\\y^2=25+30\\\\y^2=55\\\\y=\sqrt{55}$