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To find the size of angle \( y \) in the given right triangle, we can use trigonometric ratios. Specifically, we can use the sine, cosine, or tangent function. In this case:

- The side opposite angle \( y \) is 13.6 cm.
- The hypotenuse is 18.2 cm.

We can use the sine function, defined as:

\[
\sin(y) = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{13.6}{18.2}
\]

Now, let's calculate the value of \( y \):

\[
\sin(y) = \frac{13.6}{18.2} \approx 0.7473
\]

Now, we find \( y \) by taking the inverse sine (arcsin) of 0.7473:

\[
y = \arcsin(0.7473) \approx 48.3^\circ
\]

Rounding to the nearest integer:

\[
y \approx 48^\circ
\]

So, the size of angle \( y \) is approximately **48 degrees**.

Would you like more details, or do you have any other questions?

Here are 5 related questions:

1. How would you find angle \( y \) using the cosine function instead?
2. What would be the value of angle \( y \) if the opposite side were 10 cm instead of 13.6 cm?
3. Can you calculate the remaining angle in the triangle?
4. How would you calculate the length of the other side using the Pythagorean theorem?
5. What is the relationship between the angles in a right triangle?

**Tip:** Remember that the sum of all angles in a triangle is always 180 degrees.

Learn how to calculate the size of angle y in a right triangle using trigonometric ratios. Given the opposite side and hypotenuse, discover the steps to apply the sine function and find the angle measurement. Suitable for high school students studying trigonometry.

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