1. **State the problem:** We have a right triangle with one leg of length 3.4 cm adjacent to the 57° angle, and we want to find the hypotenuse $y$. 2. **Identify the knowns and unknowns:** The side adjacent to the 57° angle is 3.4 cm, the angle is 57°, and the hypotenuse is $y$. 3. **Formula used:** In a right triangle, the cosine of an angle is the ratio of the adjacent side to the hypotenuse: $$\cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}}$$ 4. **Apply the formula:** $$\cos(57^\circ) = \frac{3.4}{y}$$ 5. **Solve for $y$:** $$y = \frac{3.4}{\cos(57^\circ)}$$ 6. **Calculate the cosine:** $$\cos(57^\circ) \approx 0.5446$$ 7. **Substitute and compute:** $$y = \frac{3.4}{0.5446}$$ 8. **Simplify:** $$y \approx 6.243$$ 9. **Round to 2 decimal places:** $$y \approx 6.24$$ **Final answer:** The length of the hypotenuse $y$ is approximately 6.24 cm.