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In the provided diagram, we have a right triangle \( \triangle MNL \), with side lengths 3, 4, and 5. These sides represent a Pythagorean triplet, meaning the triangle is a right triangle, with:

- \( MN = 3 \) (opposite side to angle \( L \))
- \( ML = 5 \) (hypotenuse)
- \( NL = 4 \) (adjacent side to angle \( L \))

We are tasked with finding the values of \( \cos L \), \( \sin L \), and \( \tan L \).

1. **Cosine** is the ratio of the adjacent side to the hypotenuse:
   \[
   \cos L = \frac{\text{adjacent}}{\text{hypotenuse}} = \frac{NL}{ML} = \frac{4}{5}
   \]
   So, \( \cos L = \frac{4}{5} \).

2. **Sine** is the ratio of the opposite side to the hypotenuse:
   \[
   \sin L = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{MN}{ML} = \frac{3}{5}
   \]
   So, \( \sin L = \frac{3}{5} \).

3. **Tangent** is the ratio of the opposite side to the adjacent side:
   \[
   \tan L = \frac{\text{opposite}}{\text{adjacent}} = \frac{MN}{NL} = \frac{3}{4}
   \]
   So, \( \tan L = \frac{3}{4} \).

### Final answers:
- \( \cos L = \frac{4}{5} \)
- \( \sin L = \frac{3}{5} \)
- \( \tan L = \frac{3}{4} \)

Let me know if you need further details or explanations! Here are some related questions to explore:

1. How do you calculate the cosine of an angle in other triangles?
2. What is the relationship between sine and cosine for complementary angles?
3. How can the Pythagorean identity be used with \( \sin L \) and \( \cos L \)?
4. How can we find the other angles in the triangle using trigonometry?
5. What is the secant of angle \( L \) in this triangle?

**Tip:** The ratios between the sides of a right triangle (sine, cosine, tangent) are always related to the angle measurements. Make sure to memorize their definitions!

Use the side lengths 3, 4, and 5 of a right triangle to find cos L, sin L, and tan L.

Explore how to calculate the cosine, sine, and tangent of an angle in a 3-4-5 right triangle. This lesson explains the use of the Pythagorean theorem to verify triangle dimensions and the basic trigonometric ratios: cosine, sine, and tangent.

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