Question

A) A 20-foot ladder leans against a wall so that the ladder's angle of elevation is 46°. Find x, the distance from the base of the ladder to the building. (1 point) (2 points) Item 9 Item 10 Item 11 Ox=43.23 ft. Itern 12 28.79 ft. Item 13 13.89 ft. Item 14 Oz14.39 ft.

Answer 1

To find the distance \( x \) from the base of the ladder to the wall (building), we can use the cosine of the angle of elevation which is given as 46°. The ladder serves as the hypotenuse of a right triangle formed with the wall.

The relationship based on the cosine of the angle is given by:

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

In this case:
- \(\theta = 46°\)
- The hypotenuse is the length of the ladder, which is 20 feet.
- The adjacent side is the distance \( x \) from the base of the ladder to the wall.

Thus, we have:

\[
\cos(46°) = \frac{x}{20}
\]

To find \( x \):

\[
x = 20 \cdot \cos(46°)
\]

Now, using a calculator to compute \( \cos(46°) \):

\[
\cos(46°) \approx 0.6947
\]

Now substitute this value back into the equation:

\[
x \approx 20 \cdot 0.6947 \approx 13.894 \text{ feet}
\]

Rounding this gives:

\[
x \approx 13.89 \text{ feet}
\]

So, the distance from the base of the ladder to the building is approximately **13.89 ft**.