We are given a triangle with the following information: - Hypotenuse = 9 cm - One angle = 55 degrees - Opposite side = x - Adjacent side = y - x = 7.372 cm. We need to find the value of $y$.

1. Problem Description

We are given a triangle with the following information:

- Hypotenuse = 9 cm

- One angle = 55 degrees

- Opposite side = x

- Adjacent side = y

- x = 7.372 cm.

We need to find the value of $y$.

2. Solution Steps

We can use trigonometric ratios to relate the given angle, hypotenuse, and adjacent side.

The cosine function relates the adjacent side and hypotenuse:

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

In our case, $\theta = 55$ degrees, hypotenuse = 9 cm, and adjacent side = $y$.

So we have:

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

To find $y$, we multiply both sides by 9:

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

$cos(55^{\circ}) \approx 0.5736$

$y = 9 \times 0.5736 = 5.1624$

We can also use the Pythagorean theorem to find $y$, given $x=7.372$ and hypotenuse=

9. $x^2 + y^2 = 9^2$

$y^2 = 9^2 - x^2$

$y^2 = 81 - (7.372)^2$

$y^2 = 81 - 54.346384$

$y^2 = 26.653616$

$y = \sqrt{26.653616} \approx 5.1627$

Since we are given that $x$ is the opposite side, $x = 9*sin(55)$. $sin(55) = 0.8192$. Therefore, $x = 9*0.8192 = 7.3728$, which is close to $x = 7.372$.

3. Final Answer

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