Question

screenshot below

Answer 1

These are all right triangles. We can use the Pythagorean theorem to relate all of the sides of a right triangle:
\[a^2 + b^2 = c^2\]
In the screenshot below, I edited your problem and labeled two sides for the explanation.
We can first find side 'x':
\[x^2 + 5^2 = 6^2\]
\[x = \sqrt{11}\]
^ Be sure to check the math
Now we can solve the smaller triangle on the left hand side for side 'y'
\[\left( 6-z \right)^2 + y^2 = \left( \sqrt{11} \right)^2\]
\[y = \sqrt{-25 + 12z - z^2}\]
^ Again, check the math and make sure you know how to do it.
Now you should be able to solve for z.

Answer 2

I dont understand how to solve the last part

Answer 3

You have another right triangle which you can solve by using the Pythagorean theorem.
\[y^2 + z^2 = 5^2\]
All you have to do is plug in what y is and solve for z.