A 20-foot ladder leans against a wall so that the ladder's angle of elevation is 46°. Find how far the base of the ladder is from the wall rounded to the nearest hundredth.
The nearest hundredth of 20 tan 46° is 13.89, so the answer is $\boxed{13.89 \text{ ft}}$.
The triangle formed by the ladder, wall, and ground is a right triangle where the ladder is the hypotenuse, the wall is the opposite side, and the ground is the adjacent side. Using the definition of the tangent, $\tan \theta = \frac{\text{opposite}}{\text{adjacent}} = \frac{x}{20}$, we find $\tan 46^\circ = \frac{x}{20}$. Solving for $x$ gives $x=20\tan 46^\circ\approx \boxed{14.98}$ to the nearest hundredth.
options are:
13.89 ft
13.89 ft
28.79 ft.
28.79 ft.
14.39 ft
14.39 ft
43.23 ft