https://file.aiquickdraw.com/mathbot/file/1726621386896i0qwlgw0.jpg

The image you uploaded shows a right-angled triangle \( \triangle KLM \) with angle \( \angle L \) as the right angle. The task is to identify which of the trigonometric statements about the triangle is correct.

The trigonometric identities for a right-angled triangle are as follows:

- \( \sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}} \)
- \( \cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}} \)
- \( \tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} \)

In \( \triangle KLM \):
- \( KL \) is the adjacent side to \( \angle K \) and opposite to \( \angle M \),
- \( LM \) is the adjacent side to \( \angle M \) and opposite to \( \angle K \),
- \( KM \) is the hypotenuse.

Now, let's analyze each option:

1. **Option a: \( \cos L = \frac{KM}{LM} \)**  
   Incorrect. Since \( \angle L \) is the right angle, \( \cos L \) is undefined.

2. **Option b: \( \sin L = \frac{LM}{KL} \)**  
   Incorrect. \( \sin L \) is also undefined as \( \angle L \) is a right angle.

3. **Option c: \( \tan L = \frac{LM}{KM} \)**  
   Incorrect. \( \tan L \) is undefined since \( \angle L \) is \( 90^\circ \).

4. **Option d: \( \cos K = \frac{KM}{KL} \)**  
   Incorrect. \( \cos K = \frac{KL}{KM} \), not \( \frac{KM}{KL} \).

5. **Option e: \( \sin K = \frac{KL}{KM} \)**  
   Correct! \( \sin K \) is indeed \( \frac{\text{opposite side} (KL)}{\text{hypotenuse} (KM)} \).

Thus, the correct answer is **e**: \( \sin K = \frac{KL}{KM} \).

Would you like any further explanation or details on this? Here are some related questions to expand your understanding:

1. What is the value of \( \cos K \) in this triangle?
2. How would you calculate \( \tan K \) using the sides of the triangle?
3. Why are trigonometric functions undefined for a right angle?
4. What is the relationship between \( \sin \) and \( \cos \) for complementary angles in a triangle?
5. Can you derive \( \tan K \) using \( \sin K \) and \( \cos K \)?

**Tip:** Always remember that trigonometric functions like sine, cosine, and tangent are undefined for a 90-degree angle.

Perhatikan segitiga KLM di bawah! Berikut pernyataan yang benar adalah...

Understand how to apply trigonometric ratios like sine, cosine, and tangent in a right-angled triangle. This example uses triangle KLM to explore the correct trigonometric relationships between the sides of the triangle. Suitable for Grades 9-11.

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