https://file.aiquickdraw.com/mathbot/file/172918920251791cpfg7a.jpg

The triangle in the image appears to be a right triangle with points \( K \), \( L \), and \( M \), where:

- \( k = 5 \text{cm} \) is the length of side \( KL \).
- \( \angle KLM = 30^\circ \).

We need to find the lengths of sides \( l \) (which is \( MK \)) and \( x \) (which is \( ML \)).

### Step 1: Find \( x \)
Using the properties of a 30-60-90 triangle, where the hypotenuse is twice the length of the shorter leg:
1. The hypotenuse here is \( KL = 5 \text{cm} \).
2. Therefore, the shorter leg \( ML \) is given by:
   \[
   x = \frac{5}{2} = 2.5 \text{cm}.
   \]

### Step 2: Find \( l \)
In a 30-60-90 triangle, the length of the longer leg is \( \sqrt{3} \) times the shorter leg:
   \[
   l = 2.5 \times \sqrt{3} \approx 4.33 \text{cm}.
   \]

Thus, the sides are:
- \( x = 2.5 \text{cm} \).
- \( l \approx 4.33 \text{cm} \).

Would you like further details or have any questions? 

### Related Questions:
1. How would the calculations change if \( \angle KLM \) were \( 45^\circ \)?
2. What are the properties of a 30-60-90 triangle?
3. Can you find the area of triangle \( KLM \)?
4. What is the relationship between the sides of a 45-45-90 triangle?
5. How do trigonometric ratios apply to solving this problem?

### Tip:
In a 30-60-90 triangle, the hypotenuse is always twice the length of the shorter leg, and the longer leg is \( \sqrt{3} \) times the shorter leg.

In triangle KLM, side KL = 5 cm, angle KLM = 30°. Find the lengths of sides MK (l) and ML (x).

Solve the problem involving triangle KLM with a hypotenuse of 5 cm and a 30° angle. Learn how to find the lengths of sides MK and ML using the 30-60-90 triangle theorem, applying essential trigonometry and geometry concepts. Suitable for students in Grades 8-10.

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