To solve this problem, we need to calculate the angle $y$ in the given triangle using trigonometry.

Step-by-Step Solution:

1. Identify the sides relative to the angle $y$:

   • The adjacent side to $y$ is $9.6 \, \text{cm}$.
   • The hypotenuse is $10.7 \, \text{cm}$.

2. Use the cosine ratio: The cosine of an angle is defined as: $\cos(y) = \frac{\text{adjacent}}{\text{hypotenuse}}$ Substituting the given values: $\cos(y) = \frac{9.6}{10.7}$

3. Calculate $\cos(y)$: $\cos(y) = 0.8972 \, (\text{approximately})$

4. Find the angle $y$: To find $y$, take the inverse cosine ($\cos^{-1}$): $y = \cos^{-1}(0.8972)$

   Using a calculator: $y \approx 26^\circ \, (\text{to the nearest degree})$

Final Answer:

The angle $y$ is approximately 26 degrees.

Would you like a detailed explanation of the construction process, or do you have any further questions? 😊

Related Questions:

1. How would you construct this triangle with a compass and straightedge?
2. What trigonometric ratio would be used to find the angle if the opposite side was given instead of the adjacent side?
3. Can you calculate the other non-right angle in the triangle?
4. How would rounding the sides to fewer decimal places affect the accuracy of the angle measurement?
5. Could you verify this result using the sine or tangent functions?

Tip:

Always ensure your calculator is set to the correct mode (degrees or radians) when solving trigonometric problems!