To solve the given problem:

We are solving for the missing side $x$ in the right triangle. The known values are:

• The hypotenuse = 14
• The angle = $59^\circ$

Step-by-Step Solution:

1. Identify the sides:

   • $x$ is the adjacent side to the given angle ($59^\circ$).
   • The hypotenuse is 14.

2. Use the cosine function: The cosine function is defined as: $\cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}}$ Plugging in the values: $\cos(59^\circ) = \frac{x}{14}$

3. Solve for $x$: Multiply both sides by 14 to isolate $x$: $x = 14 \cdot \cos(59^\circ)$

4. Calculate: Using a calculator: $\cos(59^\circ) \approx 0.515$ Therefore: $x = 14 \cdot 0.515 = 7.21$

Final Answer:

The missing side $x$ is approximately 7.2 (rounded to the nearest tenth).

Would you like further clarifications or explanations? Here are some related questions for practice:

1. How would you solve for the other leg using the sine function?
2. What if the angle were changed to $45^\circ$, how would the result change?
3. Can you calculate the area of the triangle with these dimensions?
4. How do trigonometric functions relate to the Pythagorean theorem?
5. How would you calculate the hypotenuse if given the legs instead?

Tip: Always check that your calculator is set to degrees (not radians) when solving trigonometric problems involving angles in degrees.