Question

A 15-foot ladder leans against a wall so that the ladder's angle of elevation is 42° . Find x, the distance from the base of the ladder to the building. (Hint: Draw it out!)(1 point) Responses x = 22.42 ft x = 22.42 ft x = 10.04 ft x = 10.04 ft x = 11.15 ft x = 11.15 ft x = 20.18 ft

Answer 1

To find the distance \( x \) from the base of the ladder to the building, we can use trigonometric functions. Given a right triangle formed by the ladder, the wall, and the ground, we can use the cosine of the angle of elevation.

1. The length of the ladder is \( 15 \) feet (this is the hypotenuse).
2. The angle of elevation is \( 42^\circ \).

Using the cosine function:

\[
\cos(\theta) = \frac{\text{adjacent side}}{\text{hypotenuse}}
\]

In this case, the adjacent side is \( x \) (the distance from the ladder to the building), and the hypotenuse is \( 15 \) feet:

\[
\cos(42^\circ) = \frac{x}{15}
\]

Now, we can solve for \( x \):

\[
x = 15 \times \cos(42^\circ)
\]

Calculating the cosine of \( 42^\circ \):

\[
\cos(42^\circ) \approx 0.7431
\]

Now substituting this value into our equation:

\[
x \approx 15 \times 0.7431 \approx 11.15 \text{ feet}
\]

Therefore, the distance from the base of the ladder to the building \( x \) is approximately **11.15 feet**. The correct response is:

**x = 11.15 ft**.