Question

Which answer is correct?
A 16-foot ladder leans against a wall so that the ladder's angle of elevation is 55. Find x the distance between the foot of the ladder and the base of the building. Use cosine to solve for the missing side and round your answer to the nearest hundredth
x = 9.18ft
x = 27.90ft
x = 52.87ft
x = 13.11ft

Answer 1

To find the distance \( x \) between the foot of the ladder and the base of the building using cosine, we can apply the cosine function in the context of a right triangle.

In this case:
- The length of the ladder (hypotenuse) is 16 feet.
- The angle of elevation is 55 degrees.

Using the cosine function:

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

Here, the adjacent side is \( x \) (the distance from the foot of the ladder to the wall) and the hypotenuse is 16 feet.

So we can write:

\[
\cos(55^\circ) = \frac{x}{16}
\]

Now, rearranging to solve for \( x \):

\[
x = 16 \cdot \cos(55^\circ)
\]

Calculating \( \cos(55^\circ) \):

\[
\cos(55^\circ) \approx 0.5736
\]

Now substitute back to find \( x \):

\[
x \approx 16 \cdot 0.5736 \approx 9.1776 \text{ feet}
\]

Rounding to the nearest hundredth:

\[
x \approx 9.18 \text{ feet}
\]

So, the correct answer is:

**x = 9.18 ft**