Answer:
[tex]y=\sqrt{55}[/tex]
which agrees with answer A
Step-by-step explanation:
Notice there are three right angle triangles for which we can apply the Pythagorean theorem:
In the small triangle at the bottom we have the Pythagorean theorem rendering:
(a)
[tex]5^2+y^2=x^2\\x^2=25+y^2[/tex]
in the second right angle triangle on top of the previous one, if we call the vertical side on the right side "z", we have:
(b)
[tex]11^2+y^2=z^2\\z^2=121+y^2[/tex]
and finally in the large right angle triangle:
(c)
[tex]z^2+x^2=16^2\\z^2=256-x^2[/tex]
We can combine equations b and c to obtain:
[tex]121+y^2=256-x^2\\x^2+y^2=256-121=135\\x^2=135-y^2[/tex]
and then combine this and (a) to get:
[tex]25+y^2=135-y^2\\2\,y^2=135-25\\2y^2=110\\y^2=55\\y=\sqrt{55}[/tex]
