The problem describes a ladder leaning against a wall, forming a right triangle where:

• The ladder's length (hypotenuse) = 27 feet.
• The angle between the base of the ladder and the ground = 50°.
• The task is to find the distance from the base of the ladder to the wall (adjacent side).

We can use trigonometry, specifically the cosine function, which relates the adjacent side (distance from the base to the wall) to the hypotenuse (ladder's length) as follows:

$\cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}}$

Substituting the known values:

$\cos(50^\circ) = \frac{\text{adjacent}}{27}$

Solving for the adjacent side:

$\text{adjacent} = 27 \times \cos(50^\circ)$

Using $\cos(50^\circ) \approx 0.6428$:

$\text{adjacent} = 27 \times 0.6428 \approx 17.36 \text{ feet}$

Thus, the base of the ladder is approximately 17.4 feet from the wall.

This matches the option "17.4 feet."

Would you like further details or have any other questions?

Here are 5 related questions:

1. How would the problem change if the ladder was shorter or longer?
2. What if the angle was different? How would that affect the base distance?
3. Could you calculate the height the ladder reaches on the wall using sine?
4. How does the Pythagorean theorem apply to problems like this one?
5. What other real-life scenarios involve the cosine function?

Tip: When dealing with right triangles and known angles, trigonometric functions like sine, cosine, and tangent are your go-to tools for solving missing sides or angles.