You have 3 right-angled triangles so you apply the Pythagoras theorem
z^2 = 4^2 + y^2......(1)
x^2 = 6^2 + y^2 .....(2) Also taking the large triangle:-
x^2 + z^2 = 10^2.......(3)
Subtracting equation (1) from equation 2:-
x^2 - z^2 = 20 .......(4)
Adding (3) + (4):-
2x^2 = 120
x^2 = 60
x = sqrt 60
So , using equation (4) z^2 = x^2 - 20 = 60 - 20 = 40
z = sqrt 40
now we can find y by substituting in equation (1)
y^2 = z^2 - 4^2 = 40 - 16 = 24
y = sqrt 24
