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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.

Respuesta :

Answer: 12.19 ft

Step-by-step explanation:

Given

Length of ladder is [tex]23 ft[/tex]

Angle of elevation is [tex]58^{\circ}[/tex]

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

from the figure, we can write

[tex]\Rightarrow \cos 58^{\circ}=\dfrac{x}{23}\\\\\Rightarrow x=23\cos 58^{\circ}\\\Rightarrow x=12.19\ ft[/tex]

Thus, the distance is 12.19 ft

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