Answer:
The answer is : [tex]y =\sqrt{190}[/tex]
so, type 190 in the box
Step-by-step explanation:
Notice that there are three right angle triangles in the image given. In order to create equations associated with the Pythagorean Theorem for the three triangles, we add the letters x and z to identify two sides that are missing information. Please see attached image for reference.
In the small right angle triangle on the right, the Pythagorean theorem tells us:
[tex]x^2+10^2=y^2\\so\\x^2=y^2-100[/tex]
In the larger triangle :
[tex]y^2+z^2=19^2\\z^2=361-y^2[/tex]
In the small triangle on the left:
[tex]9^2+x^2=z^2[/tex]
and in this last equation we can substitute the z-squared and the x-squared by the expressions we got before in the other two equations:
[tex]9^2+(y^2-100)=(361-y^2)\\81+y^2-100= 361-y^2\\2\,y^2=361+100-81\\2\,y^2=380\\y^2=190\\[/tex]
Then to solve for "y" we apply the square root:
[tex]y =\sqrt{190}[/tex]
