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.