The image shows a trigonometry problem involving a right triangle. You are asked to find the missing side, labeled as $x$, given the angle of 59° and the adjacent side of 20 yards.

To solve this, we can use trigonometric functions. Specifically, we'll use the cosine function, which relates the adjacent side to the hypotenuse in a right triangle.

Step-by-step solution:

1. Cosine formula: $\cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}}$

   Here, $\theta = 59^\circ$, the adjacent side is 20 yards, and the hypotenuse is $x$, the missing side.

2. Rearranging the formula to solve for $x$: $x = \frac{20}{\cos(59^\circ)}$

3. Calculating: $\cos(59^\circ) \approx 0.5150$

   Now calculate $x$: $x = \frac{20}{0.5150} \approx 38.8 \text{ yards}$

Final Answer:

The missing side, $x$, is approximately 38.8 yards.

Would you like a more detailed explanation of any part of this? Or do you have another question?

Here are some related questions you might find interesting:

1. How do you solve for an unknown angle using trigonometry in a right triangle?
2. What other trigonometric functions can you use to find missing sides in right triangles?
3. How do you apply the sine and tangent functions in similar problems?
4. What is the relationship between the angles and sides in a right triangle?
5. How do you calculate the area of a right triangle when two sides are known?

Tip: Always make sure your calculator is set to the correct mode (degrees or radians) based on the problem you're solving!