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The problem is asking for the length of a ladder leaning against a vertical wall. We are given:

- The angle between the ladder and the wall is 24°.
- The distance from the foot of the ladder to the wall is 5 meters.

We can treat this situation as a right triangle, where:
- The length of the ladder is the hypotenuse (let's call it \( L \)).
- The distance from the foot of the ladder to the wall is the adjacent side (5 meters).
- The angle between the ladder and the wall is 24°.

To find the length of the ladder, we can use the cosine function:

\[
\cos(24^\circ) = \frac{\text{adjacent}}{\text{hypotenuse}} = \frac{5}{L}
\]

Rearranging the formula to solve for \( L \):

\[
L = \frac{5}{\cos(24^\circ)}
\]

Now, I'll calculate the value of \( L \).The length of the ladder is approximately 5.47 meters.

Would you like any further explanation or details about this calculation?

Here are some related questions to expand your understanding:
1. How would the length of the ladder change if the angle with the wall were increased?
2. What if the distance from the wall was doubled? How would that affect the length of the ladder?
3. Could we use the sine function instead of cosine to solve this problem?
4. How can you find the height the ladder reaches on the wall?
5. What happens if the angle is 90°?

**Tip:** In problems involving right triangles, understanding which trigonometric function to use (sine, cosine, or tangent) depends on which sides of the triangle are involved (adjacent, opposite, or hypotenuse).

A ladder leaning against a vertical wall makes an angle of 24° with the wall. The foot of the ladder is 5 m from the wall. Find the length of the ladder.

This problem involves calculating the length of a ladder leaning against a wall using trigonometry. Given an angle of 24° and a distance of 5 meters from the wall, solve for the ladder's length using the cosine function. Suitable for Grades 9-12.

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