The problem is to find the values of $x$ and $y$ in the given right triangle. We are given that the hypotenuse is 9 cm and one angle is 55 degrees. We need to find the length of the side opposite to this angle ($x$) and the length of the side adjacent to this angle ($y$).

1. Problem Description

The problem is to find the values of $x$ and $y$ in the given right triangle. We are given that the hypotenuse is 9 cm and one angle is 55 degrees. We need to find the length of the side opposite to this angle ($x$) and the length of the side adjacent to this angle ($y$).

2. Solution Steps

We can use trigonometric ratios to solve for $x$ and $y$.

To find $x$, we can use the sine function:

$sin(\theta) = \frac{opposite}{hypotenuse}$

$sin(55^{\circ}) = \frac{x}{9}$

$x = 9 \cdot sin(55^{\circ})$

To find $y$, we can use the cosine function:

$cos(\theta) = \frac{adjacent}{hypotenuse}$

$cos(55^{\circ}) = \frac{y}{9}$

$y = 9 \cdot cos(55^{\circ})$

Using a calculator, we can find the values of $sin(55^{\circ})$ and $cos(55^{\circ})$:

$sin(55^{\circ}) \approx 0.819$

$cos(55^{\circ}) \approx 0.574$

Therefore,

$x = 9 \cdot 0.819 = 7.371$

$y = 9 \cdot 0.574 = 5.166$

3. Final Answer

$x = 9sin(55^{\circ})$

$y = 9cos(55^{\circ})$