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 = 10.04 ft
x = 10.04 ft

x = 22.42 ft
x = 22.42 ft

x = 11.15 ft
x = 11.15 ft

x = 20.18 ft

Answer 1

To solve for \( x \), the distance from the base of the ladder to the building, you can use the cosine function from trigonometry, since you have the length of the ladder and the angle of elevation.

Given:
- Length of the ladder, \( L = 15 \) feet
- Angle of elevation, \( \theta = 42^\circ \)

You can use the cosine of the angle:
\[
\cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}}
\]

In this case, the adjacent side is \( x \) and the hypotenuse is the length of the ladder:
\[
\cos(42^\circ) = \frac{x}{15}
\]

Now, solve for \( x \):
\[
x = 15 \cdot \cos(42^\circ)
\]

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

Now plug in the value:
\[
x \approx 15 \cdot 0.7431 \approx 11.15 \text{ feet}
\]

Thus, the value of \( x \) is:
\[
\boxed{11.15 \text{ ft}}
\]