We are given a right triangle with one angle of $54^{\circ}$ and the side opposite to the angle equal to 32. We need to find the length of the adjacent side, which is labeled as $x$. We must round our answer to the nearest tenth.

1. Problem Description

We are given a right triangle with one angle of $54^{\circ}$ and the side opposite to the angle equal to

3

2. We need to find the length of the adjacent side, which is labeled as $x$. We must round our answer to the nearest tenth.

2. Solution Steps

We can use the tangent function to relate the angle to the opposite and adjacent sides.

The tangent function is defined as:

$tan(\theta) = \frac{opposite}{adjacent}$

In this case, $\theta = 54^{\circ}$, the opposite side is 32, and the adjacent side is $x$.

So, we have:

$tan(54^{\circ}) = \frac{32}{x}$

Now, we can solve for $x$:

$x = \frac{32}{tan(54^{\circ})}$

Using a calculator, we find that $tan(54^{\circ}) \approx 1.37638$.

$x \approx \frac{32}{1.37638} \approx 23.249$

Rounding to the nearest tenth, we get $x \approx 23.2$.

3. Final Answer

23.2