1. Apply the Pythagorean theorem:  c = \sqrt{a^2 + b^2}  .
2. Substitute \( a = 19.1 \) and \( b = 16.2 \):
 c = \sqrt{{19.1}^2 + {16.2}^2}  .
3. Calculate the squares: 
 {19.1}^2 = 364.81  ,
 {16.2}^2 = 262.44  .
4. Add the squares: 
 364.81 + 262.44 = 627.25  .
5. Take the square root:
\sqrt{627.25}\approx25.044 .
The length of the hypotenuse is approximately 25.044 .