To solve for $x$ in this right triangle, we use trigonometric ratios. Specifically, since we are given the hypotenuse (13) and are solving for the adjacent side relative to the $47^\circ$ angle, we apply the cosine function.

Step-by-step solution:

1. Identify the trigonometric ratio: $\cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}}$ Here:

   • $\theta = 47^\circ$,
   • adjacent side = $x$,
   • hypotenuse = 13.

   Substituting into the formula: $\cos(47^\circ) = \frac{x}{13}$

2. Solve for $x$: Rearranging for $x$: $x = 13 \cdot \cos(47^\circ)$

3. Evaluate using a calculator: $\cos(47^\circ) \approx 0.682$ Then: $x = 13 \cdot 0.682 \approx 8.9$

Final Answer:

$x \approx 8.9 \, \text{units (rounded to the nearest tenth).}$

Do you want a further explanation of the steps or a breakdown of trigonometric functions? Let me know!

Related Questions:

1. How do you find the opposite side in this triangle?
2. What is the value of the sine of $47^\circ$ in this triangle?
3. How do you verify the hypotenuse using the Pythagorean theorem?
4. How do you calculate the missing angle in the triangle?
5. What are the steps to solve for the opposite side if $x$ is known?

Tip: Always confirm which trigonometric function (sine, cosine, or tangent) matches the given sides in a triangle.