Congruent triangles are exactly the same, meaning they have the same side length, and thus same angles. Everything is exactly the same, as easy as it gets :)
So, you can compare the two pictures to get the informations you need:
[tex] x = 90^\circ [/tex], since it is a right angle
[tex] y = 38^\circ [/tex], as we can see on the right by comparison
[tex] w = 52^\circ [/tex]. In fact, the angles of a triangle sum to [tex] 180^\circ [/tex], so we have [tex] x+y+w = 90+38+w = 128+w = 180[/tex]. So, [tex] w = 180-128 = 52[/tex]
[tex] v = 7.9 [/tex]yd, as we can see on the left by comparison.
Finally, we can compute [tex] z [/tex] using the Pythagorean theorem:
[tex] z = \sqrt{u^2+v^2} = \sqrt(6.2^2+7.9^2) \approx 10 [/tex]
