Question

A 23 foot ladder is leaning against a wall. The angle of elevation of the ladder with the ground is `58\ degrees.` How far away is the bottom of the ladder from the bottom of the wall? Round your answer to the nearest hundredth.

Answer 1

Answer: 12.19 ft

Explanation:

Given

Length of ladder is
`23 ft`

Angle of elevation is
`58^(\circ)`

Suppose the bottom of the ladder is x ft away from the bottom of the wall

from the figure, we can write

`\Rightarrow \cos 58^(\circ)=(x)/(23)\\\\\Rightarrow x=23\cos 58^(\circ)\\\Rightarrow x=12.19\ ft`

Thus, the distance is 12.19 ft