Answer:
5.18 feet
Step-by-step explanation:
We have been given that a ladder that is 20 feet long is leaning against the side of a building if the angle formed between the ladder and the ground is 75 degrees.
We can see from the attachment that side with 20 feet is hypotenuse and side x is adjacent side to the angle 75 degrees.
[tex]\text{cos}=\frac{\text{Adjacent}}{\text{Hypotenuse}}[/tex]
Substitute the given values:
[tex]\text{cos}(75^{\circ})=\frac{x}{20}[/tex]
[tex]\frac{x}{20}=\text{cos}(75^{\circ})[/tex]
[tex]\frac{x}{20}*20=20*\text{cos}(75^{\circ})[/tex]
[tex]x=20*0.258819045103[/tex]
[tex]x=5.1763809[/tex]
[tex]x\approx 5.18[/tex]
Therefore, the bottom of the ladder is 5.18 feet away from the base of the building.
