To solve for $y$, we use the Pythagorean theorem in the right triangle provided. The formula is:

$y^2 = (7.7)^2 - (4)^2$

Step 1: Compute squares of the sides

$7.7^2 = 59.29 \quad \text{and} \quad 4^2 = 16$

Step 2: Subtract to find $y^2$

$y^2 = 59.29 - 16 = 43.29$

Step 3: Take the square root of $y^2$

$y = \sqrt{43.29} \approx 6.6$

Final Answer:

$y \approx 6.6 \, \text{(rounded to 1 decimal place)}$

Would you like further details or explanation?

Here are 5 related questions for practice:

1. What is the Pythagorean theorem, and how is it used in other scenarios?
2. How do you find the hypotenuse given the other two sides?
3. What would happen if one side of the triangle were missing? How would you find it?
4. How do you calculate squares and square roots without a calculator?
5. Why is rounding to 1 decimal place useful in this context?

Tip: Always double-check units and rounding instructions to ensure accuracy in applied math problems!