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We are given a right triangle \( \triangle JKL \), where:

- \( \angle J = 59^\circ \)
- The side adjacent to the angle (JL) is 15 units
- The hypotenuse (x) is the unknown value we need to find

To solve for \( x \), we can use the **cosine** function since it relates the adjacent side and the hypotenuse.

### Step-by-Step Solution:
\[
\cos(59^\circ) = \frac{\text{adjacent}}{\text{hypotenuse}}
\]
\[
\cos(59^\circ) = \frac{15}{x}
\]

Now, solve for \( x \):
\[
x = \frac{15}{\cos(59^\circ)}
\]

Using a calculator:
\[
\cos(59^\circ) \approx 0.5150
\]
\[
x = \frac{15}{0.5150} \approx 29.13
\]

### Final Answer:
\[
x \approx 29.13
\]

Let me know if anything needs further clarification!

---

Would you like to explore the following?

1. What if the given angle were \(30^\circ\)? How would the solution change?
2. How do sine and tangent functions relate to this same problem?
3. How can you find the other side (KL) using trigonometry?
4. What happens if the triangle was not a right triangle? How would we solve for \( x \)?
5. Why is cosine used here, and not sine or tangent?

**Tip:** For precision in trigonometry problems, always ensure your calculator is in degree mode!

Find the value of x in the right triangle with an angle of 59° and adjacent side 15. Round your answer to two decimal places.

Calculate the hypotenuse in a right triangle with a 59° angle and a side of 15 using the cosine function. Perfect for Grade 9-10 students studying trigonometry.

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