Both right triangles share the same leg we'll call "b". Pythagorean theorem
a² + b² = h²
Smaller triangle .
3² + b² = (√34)²
b² = 34 - 9
b² = 25
b = 5
Larger triangle.
x² + 5² = 11²
x² + 25 = 121
x² = 121 - 25
x² = 96
x = √(96)
factor out any perfect squares from 96
x = √(16*6)
x = 4√(6)
