Question

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)

Answer 1

To find the distance from the base of the ladder to the building, you can use trigonometry. Specifically, you can use the cosine function, which relates the angle of elevation to the adjacent side (the distance from the base of the ladder to the building) and the hypotenuse (the length of the ladder).

In this case, let \( x \) be the distance from the base of the ladder to the building. The cosine of the angle of elevation (46°) can be expressed as:

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

Substituting the known values:

\[
\cos(46°) = \frac{x}{20}
\]

To find \( x \), rearranging the equation gives:

\[
x = 20 \cdot \cos(46°)
\]

Now, calculating \( x \):

1. Calculate \( \cos(46°) \):
\[
\cos(46°) \approx 0.6947 \quad (\text{using a calculator})
\]

2. Now plug this value into the equation:
\[
x = 20 \cdot 0.6947 \approx 13.894
\]

Thus, the distance from the base of the ladder to the building is approximately:

\[
\boxed{13.89 \text{ feet}}
\]